The document proves the algebraic identity a3 - b3 = (a - b)(a2 + ab + b2) using unit cubes. It takes values of a = 3 and b = 1. It represents each term of the identity using cubes and cuboids of unit cubes: a3 as a 3x3x3 cube; b3 as a 1x1x1 cube; a3 - b3 as their difference; and the terms of (a - b)(a2 + ab + b2) as cuboids. It is observed that the number of unit cubes in a3 - b3 equals the number in (a - b)(a2 + ab + b2), proving the identity.