Boundary Values & Fourier Series · Superchallenge problem

Find the Fourier series of $f(x) = x(\pi^2 - x^2)$ on $[-\pi,\pi]$ and use Parseval's identity $\dfrac1\pi\displaystyle\int_{-\pi}^{\pi}f^2\,dx = \dfrac{a_0^2}{2} + \sum(a_n^2 + b_n^2)$ to find $\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n^6}$.