Use the divergence theorem to calculate the flux of the vector field $\vec{F}(x,y,z) = 2 x y \vec{i} + z^{6} \vec{j} + 3 y \vec{k}$ through the outward-oriented, closed box $S$ given by


$\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A} =$