Diagonals in an n-cube

Take a unit n-cube (an n dimensional analogue of a cube) in $d$ dimensions. The length of the longest segment connecting two points in the cube, or longest diagonal, is $D$ . Let $S$ be the sum of all the distinct diagonals of length $D$ . For this particular dimension, you are given that

$\frac { { S }^{ 2 } }{ d } =64$

What is $d$ ?