so i believe the volume of a cube using space diagonals is

V = d^3 / 3sqrt(3) where d is the space diagonal

can anyone help me prove this? the question this relates to is actually the volume of a rectangular prism in terms of space diagonal, but to understand the cube scenario would be a good starter.

apologies for not using latex, i havent used it in a while and need to re-educate myself

thankyou in advance