Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $\mathbf F = (3x - x^3,\ 3y - y^3,\ 3z - z^3)$. Among all closed surfaces $S$ bounding a solid region (with outward normal), find the largest possible value of the flux $\iint_S \mathbf F\cdot d\mathbf S$. Give an exact answer.