 Inertia tensor of a uniform cube

For a uniform cube of side $s$ and mass $M$, reflection symmetry makes central off-diagonal inertia components zero. Equal coordinate second moments are $⟨x^2⟩=⟨y^2⟩=⟨z^2⟩=s^2/12$, so each diagonal component is $M{s}^2/6$. Thus every central axis is a principal axis. A nonspherical shape can have an isotropic central inertia tensor: that tensor measures only quadratic moments of the mass distribution, not the whole shape.