Moment of Inertia of a Cube

This calculation is for the moment of inertia of a cube.  For the purposes of this calculation, a cube can have three equal sides or it can have three non-equal sides.  The moment of inertia is calculated three different ways, about the center of the I_height, I_width and about the end I_length directions: Z-axis, Y-axis and X-axis, respectively.

\(\large{ I_h = \frac {1}{12} \; m \; \left( l^2  + w^2 \right) }\) \(\large{ I_l = \frac {1}{12} \; m \; \left( h^2  + w^2 \right) }\) \(\large{ I_w = \frac {1}{12} \; m \; \left( l^2  + h^2 \right) }\) Where: \(\large{ I }\) = moment of inertia \(\large{ h }\) = height \(\large{ l }\) = length \(\large{ m }\) = mass \(\large{ w }\) = width