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We present some variations on the theme of “cubes”. We start with right and wrong ways to draw cubes and orthogonal axes. From there we classify cubes in 3-space with integral coordinates. Further, we find that four complex numbers are the vertices of a drawing of a regular tetrahedron if their average of squares equals the square of their average. Tangentially, we find short proofs of the Siebeck-Marden theorem and a method for solving a cubic equation. Finally, we consider sets of complex numbers whose average of squares equals the square of their average.

Drawing Cubes, Finding Integral Cubes, and Solving Cubics