Boundary Values & Fourier Series · Challenge problem

The sine series of $x(\pi - x)$ on $[0,\pi]$ is $\dfrac8\pi\sum_{n\ \mathrm{odd}}\dfrac{\sin nx}{n^3}$. Use Parseval's identity for sine series, $\dfrac2\pi\displaystyle\int_0^\pi f^2\,dx = \sum b_n^2$, to find $\displaystyle\sum_{k=0}^{\infty}\dfrac{1}{(2k+1)^6}$.