Sol LeWitt (1928-2007) made or designed several artworks whose titles contain the phrase “three-part variations on three different kinds of cubes.” To a mathematician, these pieces suggest a combinatorics problem: How many variations are there? In this paper we present a new way of diagramming LeWitt’s variations, we describe how to solve the combinatorics problem using Burnside’s Counting Theorem, and we share some photos of our 3D-printed versions of the variations, including a new 57th variation.