The moment of inertia of a magic square in defined as the sum over all cells of

**(the number in the cell) times (the squared distance from the center of the cell to the center of the magic square)**; where the unit of measurement is the width of one cell.

Example: a corner cell of a 3×3 square has a distance of sqrt(2), a non-corner edge cell has a distance of 1, and the center cell has a distance of 0.

Clearly, all magic squares of a given order have the same moment of inertia

as each other.

For the order-3 case the moment of inertia is always 60, while for the order-4 case the moment of inertia is always 340.

Derive the formula for the ** nxn** case.