This document proves the algebraic identity (a-b)3 = a3 - 3a2b + 3ab2 - b3 using unit cubes. It takes values of a=3 and b=1, and represents each term of the identity as cubes and cuboids. By building and then taking apart the shapes, it shows that the number of unit cubes in both (a-b)3 and a3 - 3a2b + 3ab2 - b3 is equal, proving the identity.