Show that an object's inertia tensor about a point displaced from the centre of mass by a vector $\mathbf{c}$ is given by

$$\left(I_{\mathbf{c}}\right)_{a b}=\left(I_{0}\right)_{a b}+M\left(|\mathbf{c}|^{2} \delta_{a b}-c_{a} c_{b}\right),$$

where $M$ is the total mass of the object, and $\left(I_{0}\right)_{a b}$ is the inertia tensor about the centre of mass.

Find the inertia tensor of a cube of uniform density, with edge of length $L$, about one of its vertices.