Use the divergence theorem to calculate the flux of the vector field $\vec{F}(x,y,z) = x^{3} \vec{i} + (3 y - 3 x^{2} y) \vec{j} + 6 z \vec{k}$ through the sphere $S$ of radius $5$ centered at the origin and oriented outward.
$\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A} =$