The design problem spans art and mathematics. Its subproblems make incursions into science. We begin by stating, what the problem is -- a set of algorithms .that enable us to create a three-dimensional, composite, pleasant, geometrical design on a set of Rubik's cubes. We explain parity pairs, which influence design symmetry. We actually construct a simple design, the Menger Sponge. We conclude this article with some observations about fractals. The nature of the Rubik's cube makes it possible to create designs which mimic fractals.