Surface Integrals, Stokes & Divergence · Hard problem

Inside a solid ball of radius $2$ m there is both a continuous source with $\nabla\cdot\mathbf F=6$ everywhere and a single point source at the center that, by itself, contributes exactly $4\pi$ to the outward flux through ANY surface enclosing it (as for an inverse-square field). Find the total outward flux of $\mathbf F$ through the sphere $x^2+y^2+z^2=4$.