Stokes & Divergence theorems

Homework Statement

Given F = xyz i + (y^2 + 1) j + z^3 k
Let S be the surface of the unit cube 0 ≤ x, y, z ≤ 1. Evaluate the surface integral ∫∫(∇xF).n dS using
a) the divergence theorem
b) using Stokes' theorem

Homework Equations

Divergence theorem:
∫∫∫∇.FdV = ∫∫∇.ndS

Stokes theorem:
∫∫(∇xF).n dS = ∫F.dR

The Attempt at a Solution

The divergence theorem gives a dot product. Here we're asked for the cross product
∫∫(∇xF).n dS
but the divergence of the curl will be 0. The Stokes theorem applied here is nonzero. What's wrong?