Box-shaped prisms inside a 5 by 5 by 5 cube

A transparent cube is divided into a $5\times5\times5$ grid of unit cubes. How many rectangular boxes, with edges along the grid lines, can be found inside it? Boxes in different positions count separately (so a $4\times4\times4$ cube contains eight $3\times3\times3$ cubes).

$3375$. A box is fixed by choosing two of the $6$ grid planes in each of the three directions, giving $\binom62^3=15^3=3375$.