Use the divergence theorem to calculate the flux of the vector field $\vec{F}(x,y,z) = x^3 \vec{i} + y^3 \vec{j} + z^3 \vec{k}$ out of the closed, outward-oriented surface $S$ bounding the solid $x^2 + y^2 \leq 4, \ 0 \leq z \leq 6.$
$\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A} =$