Surface Integrals, Stokes & Divergence · Challenge problem

Let $\mathbf F = \dfrac{(x, y, z)}{(x^2 + y^2 + z^2)^{3/2}}$ (the inverse-square field, defined away from the origin). Find the outward flux of $\mathbf F$ through the surface of the cube $-1 \le x, y, z \le 1$. Give an exact answer in terms of $\pi$.