$sum_{n=1}^inftyfrac1{n^6}=frac{pi^6}{945}$ by Fourier series of $x^2$

Prove that
$$\sum_{n=1}^\infty\frac1{n^6}=\frac{\pi^6}{945}$$ by the Fourier series of $x^2$.

By Parseval's identity, I can only show $\sum_{n=1}^\infty\frac1{n^4}=\frac{\pi^4}{90}$. Could you please give me some hints?