Sum of series sin(n*x)/n^3

sin(2*x)   sin(3*x)   sin(4*x)   sin(5*x)   sin(6*x)   sin(7*x)   sin(8*x)   sin(9*x)   sin(10*x)   sin(11*x)   sin(12*x)   sin(13*x)   sin(14*x)   sin(15*x)   sin(16*x)   sin(17*x)   sin(18*x)   sin(19*x)   sin(20*x)   sin(21*x)   sin(22*x)   sin(23*x)   sin(24*x)   sin(25*x)   sin(26*x)   sin(27*x)   sin(28*x)   sin(29*x)   sin(30*x)   sin(31*x)   sin(32*x)   sin(33*x)   sin(34*x)   sin(35*x)   sin(36*x)   sin(37*x)   sin(38*x)   sin(39*x)   sin(40*x)   sin(41*x)   sin(42*x)   sin(43*x)   sin(44*x)   sin(45*x)   sin(46*x)   sin(47*x)   sin(48*x)   sin(49*x)   sin(50*x)   sin(51*x)   sin(52*x)   sin(53*x)   sin(54*x)   sin(55*x)   sin(56*x)   sin(57*x)   sin(58*x)   sin(59*x)   sin(60*x)   sin(61*x)   sin(62*x)   sin(63*x)   sin(64*x)   sin(65*x)   sin(66*x)   sin(67*x)   sin(68*x)   sin(69*x)   sin(70*x)   sin(71*x)   sin(72*x)   sin(73*x)   sin(74*x)   sin(75*x)   sin(76*x)   sin(77*x)   sin(78*x)   sin(79*x)   sin(80*x)   sin(81*x)   sin(82*x)   sin(83*x)   sin(84*x)   sin(85*x)   sin(86*x)   sin(87*x)   sin(88*x)   sin(89*x)   sin(90*x)   sin(91*x)   sin(92*x)   sin(93*x)   sin(94*x)   sin(95*x)   sin(96*x)   sin(97*x)   sin(98*x)   sin(99*x)   sin(100*x)         
-------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + --------- + ---------- + sin(x)
   8          27         64        125        216        343        512        729         1000        1331        1728        2197        2744        3375        4096        4913        5832        6859        8000        9261       10648       12167       13824       15625       17576       19683       21952       24389       27000       29791       32768       35937       39304       42875       46656       50653       54872       59319       64000       68921       74088       79507       85184       91125       97336       103823      110592      117649      125000      132651      140608      148877      157464      166375      175616      185193      195112      205379      216000      226981      238328      250047      262144      274625      287496      300763      314432      328509      343000      357911      373248      389017      405224      421875      438976      456533      474552      493039      512000      531441      551368      571787      592704      614125      636056      658503      681472      704969      729000      753571      778688      804357      830584      857375      884736      912673      941192      970299     1000000           

$$\sin{\left(x \right)} + \frac{\sin{\left(2 x \right)}}{8} + \frac{\sin{\left(3 x \right)}}{27} + \frac{\sin{\left(4 x \right)}}{64} + \frac{\sin{\left(5 x \right)}}{125} + \frac{\sin{\left(6 x \right)}}{216} + \frac{\sin{\left(7 x \right)}}{343} + \frac{\sin{\left(8 x \right)}}{512} + \frac{\sin{\left(9 x \right)}}{729} + \frac{\sin{\left(10 x \right)}}{1000} + \frac{\sin{\left(11 x \right)}}{1331} + \frac{\sin{\left(12 x \right)}}{1728} + \frac{\sin{\left(13 x \right)}}{2197} + \frac{\sin{\left(14 x \right)}}{2744} + \frac{\sin{\left(15 x \right)}}{3375} + \frac{\sin{\left(16 x \right)}}{4096} + \frac{\sin{\left(17 x \right)}}{4913} + \frac{\sin{\left(18 x \right)}}{5832} + \frac{\sin{\left(19 x \right)}}{6859} + \frac{\sin{\left(20 x \right)}}{8000} + \frac{\sin{\left(21 x \right)}}{9261} + \frac{\sin{\left(22 x \right)}}{10648} + \frac{\sin{\left(23 x \right)}}{12167} + \frac{\sin{\left(24 x \right)}}{13824} + \frac{\sin{\left(25 x \right)}}{15625} + \frac{\sin{\left(26 x \right)}}{17576} + \frac{\sin{\left(27 x \right)}}{19683} + \frac{\sin{\left(28 x \right)}}{21952} + \frac{\sin{\left(29 x \right)}}{24389} + \frac{\sin{\left(30 x \right)}}{27000} + \frac{\sin{\left(31 x \right)}}{29791} + \frac{\sin{\left(32 x \right)}}{32768} + \frac{\sin{\left(33 x \right)}}{35937} + \frac{\sin{\left(34 x \right)}}{39304} + \frac{\sin{\left(35 x \right)}}{42875} + \frac{\sin{\left(36 x \right)}}{46656} + \frac{\sin{\left(37 x \right)}}{50653} + \frac{\sin{\left(38 x \right)}}{54872} + \frac{\sin{\left(39 x \right)}}{59319} + \frac{\sin{\left(40 x \right)}}{64000} + \frac{\sin{\left(41 x \right)}}{68921} + \frac{\sin{\left(42 x \right)}}{74088} + \frac{\sin{\left(43 x \right)}}{79507} + \frac{\sin{\left(44 x \right)}}{85184} + \frac{\sin{\left(45 x \right)}}{91125} + \frac{\sin{\left(46 x \right)}}{97336} + \frac{\sin{\left(47 x \right)}}{103823} + \frac{\sin{\left(48 x \right)}}{110592} + \frac{\sin{\left(49 x \right)}}{117649} + \frac{\sin{\left(50 x \right)}}{125000} + \frac{\sin{\left(51 x \right)}}{132651} + \frac{\sin{\left(52 x \right)}}{140608} + \frac{\sin{\left(53 x \right)}}{148877} + \frac{\sin{\left(54 x \right)}}{157464} + \frac{\sin{\left(55 x \right)}}{166375} + \frac{\sin{\left(56 x \right)}}{175616} + \frac{\sin{\left(57 x \right)}}{185193} + \frac{\sin{\left(58 x \right)}}{195112} + \frac{\sin{\left(59 x \right)}}{205379} + \frac{\sin{\left(60 x \right)}}{216000} + \frac{\sin{\left(61 x \right)}}{226981} + \frac{\sin{\left(62 x \right)}}{238328} + \frac{\sin{\left(63 x \right)}}{250047} + \frac{\sin{\left(64 x \right)}}{262144} + \frac{\sin{\left(65 x \right)}}{274625} + \frac{\sin{\left(66 x \right)}}{287496} + \frac{\sin{\left(67 x \right)}}{300763} + \frac{\sin{\left(68 x \right)}}{314432} + \frac{\sin{\left(69 x \right)}}{328509} + \frac{\sin{\left(70 x \right)}}{343000} + \frac{\sin{\left(71 x \right)}}{357911} + \frac{\sin{\left(72 x \right)}}{373248} + \frac{\sin{\left(73 x \right)}}{389017} + \frac{\sin{\left(74 x \right)}}{405224} + \frac{\sin{\left(75 x \right)}}{421875} + \frac{\sin{\left(76 x \right)}}{438976} + \frac{\sin{\left(77 x \right)}}{456533} + \frac{\sin{\left(78 x \right)}}{474552} + \frac{\sin{\left(79 x \right)}}{493039} + \frac{\sin{\left(80 x \right)}}{512000} + \frac{\sin{\left(81 x \right)}}{531441} + \frac{\sin{\left(82 x \right)}}{551368} + \frac{\sin{\left(83 x \right)}}{571787} + \frac{\sin{\left(84 x \right)}}{592704} + \frac{\sin{\left(85 x \right)}}{614125} + \frac{\sin{\left(86 x \right)}}{636056} + \frac{\sin{\left(87 x \right)}}{658503} + \frac{\sin{\left(88 x \right)}}{681472} + \frac{\sin{\left(89 x \right)}}{704969} + \frac{\sin{\left(90 x \right)}}{729000} + \frac{\sin{\left(91 x \right)}}{753571} + \frac{\sin{\left(92 x \right)}}{778688} + \frac{\sin{\left(93 x \right)}}{804357} + \frac{\sin{\left(94 x \right)}}{830584} + \frac{\sin{\left(95 x \right)}}{857375} + \frac{\sin{\left(96 x \right)}}{884736} + \frac{\sin{\left(97 x \right)}}{912673} + \frac{\sin{\left(98 x \right)}}{941192} + \frac{\sin{\left(99 x \right)}}{970299} + \frac{\sin{\left(100 x \right)}}{1000000}$$

sin(2*x)/8 + sin(3*x)/27 + sin(4*x)/64 + sin(5*x)/125 + sin(6*x)/216 + sin(7*x)/343 + sin(8*x)/512 + sin(9*x)/729 + sin(10*x)/1000 + sin(11*x)/1331 + sin(12*x)/1728 + sin(13*x)/2197 + sin(14*x)/2744 + sin(15*x)/3375 + sin(16*x)/4096 + sin(17*x)/4913 + sin(18*x)/5832 + sin(19*x)/6859 + sin(20*x)/8000 + sin(21*x)/9261 + sin(22*x)/10648 + sin(23*x)/12167 + sin(24*x)/13824 + sin(25*x)/15625 + sin(26*x)/17576 + sin(27*x)/19683 + sin(28*x)/21952 + sin(29*x)/24389 + sin(30*x)/27000 + sin(31*x)/29791 + sin(32*x)/32768 + sin(33*x)/35937 + sin(34*x)/39304 + sin(35*x)/42875 + sin(36*x)/46656 + sin(37*x)/50653 + sin(38*x)/54872 + sin(39*x)/59319 + sin(40*x)/64000 + sin(41*x)/68921 + sin(42*x)/74088 + sin(43*x)/79507 + sin(44*x)/85184 + sin(45*x)/91125 + sin(46*x)/97336 + sin(47*x)/103823 + sin(48*x)/110592 + sin(49*x)/117649 + sin(50*x)/125000 + sin(51*x)/132651 + sin(52*x)/140608 + sin(53*x)/148877 + sin(54*x)/157464 + sin(55*x)/166375 + sin(56*x)/175616 + sin(57*x)/185193 + sin(58*x)/195112 + sin(59*x)/205379 + sin(60*x)/216000 + sin(61*x)/226981 + sin(62*x)/238328 + sin(63*x)/250047 + sin(64*x)/262144 + sin(65*x)/274625 + sin(66*x)/287496 + sin(67*x)/300763 + sin(68*x)/314432 + sin(69*x)/328509 + sin(70*x)/343000 + sin(71*x)/357911 + sin(72*x)/373248 + sin(73*x)/389017 + sin(74*x)/405224 + sin(75*x)/421875 + sin(76*x)/438976 + sin(77*x)/456533 + sin(78*x)/474552 + sin(79*x)/493039 + sin(80*x)/512000 + sin(81*x)/531441 + sin(82*x)/551368 + sin(83*x)/571787 + sin(84*x)/592704 + sin(85*x)/614125 + sin(86*x)/636056 + sin(87*x)/658503 + sin(88*x)/681472 + sin(89*x)/704969 + sin(90*x)/729000 + sin(91*x)/753571 + sin(92*x)/778688 + sin(93*x)/804357 + sin(94*x)/830584 + sin(95*x)/857375 + sin(96*x)/884736 + sin(97*x)/912673 + sin(98*x)/941192 + sin(99*x)/970299 + sin(100*x)/1000000 + sin(x)