List of top Mathematics Questions on Fourier series

If $f(x) = x^3$, $0 \le x \le 4$, $f(x+4) = f(x)$ $\forall x \in \mathbb{R}$ and the Fourier series of $f(x)$ is $f(x) = \sum_{n=0}^{\infty} \left(a_n \cos \frac{n\pi x}{2} + b_n \sin \frac{n\pi x}{2}\right)$, then $a_0 =$}