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 $x^2 + y^2 \le 9$, $0 \le z \le 7$.
$\iint_S \vec{F} \cdot d\vec{A} = \text{_____}$