Fourier series and reimann zeta

[hectorzer]

Homework Statement

Find the Fourier series expansion for f(x)=x^{3}, a periodic function on -\pi<x<\pi
Use this to compute \zeta(6)=\sum\frac{1}{n^{6}}

Homework Equations

Parsevals Theorom,
Real Fourier series

The Attempt at a Solution

I got the Fourier series to be \sum\frac{2(-1)^{n}(6-n^{2}\pi^{2})}{n^{3}}sin(nx)

Using Parsevals theorom I got that \frac{\pi^{6}}{7}=\sum\frac{4(6-(n\pi)^{2})^{2}}{n^{6}}

The answer is supposed to be \frac{\pi^{6}}{945} I think, I can't see where I went wrong :S
Thanks in advance :)

 

[hectorzer]

Never mind, I got it.
Just had to expand the top and use the values for the riemann zeta functions of zeta=2 and 4 and it works out :)