Parseval for the series Σ 1/n⁶

Given that the $2\pi$-periodic extension of $f(x)=x^3-{\pi }^{2}x$, $x\in [-\pi ,\pi ]$, has Fourier series

$$x^3-{\pi }^{2}x\sim \sum _{n=1}^{\infty }\frac{12(-1{)}^n}{n^3}\sin (nx),$$

compute with Parseval’s identity the sum of the series $\sum _{n=1}^{\infty }\frac{1}{n^6}$.