GR-HMS 2016 Problem 4

A square $ABCD$ is divided into $n^2$ equal small (fundamental) squares by drawing lines parallel to its sides.The vertices of the fundamental squares are called vertices of the grid.A rhombus is called nice when: $\bullet$ It is not a square $\bullet$ Its vertices are points of the grid $\bullet$ Its diagonals are parallel to the sides of the square $ABCD$ Find (as a function of $n$ ) the number of the nice rhombuses ( $n$ is a positive integer greater than $2$ ).