Let \(\mathcal{W}\) be the region between the sphere of radius 4 and the cube of side 1, both centered at the origin. What is the flux through the boundary \(\mathcal{S}=\partial \mathcal{W}\) of a vector field \(\mathbf{F}\) whose divergence has the constant value \(\operatorname{div}(\mathbf{F})=-4\) ?