Visual Sum of Cubes

This article explores a pattern for deriving formulas for the sum of cubes using four tetrahedra. The author starts by discussing how two lines are used to find the sum of squares, and then uses three triangles for the sum of cubes. The process involves arranging the numbers in a pyramid or an octahedron shape but eventually concludes that tetrahedra offer the best symmetry. The resulting formula is derived by adding four rotated copies of the tetrahedron and using the previously established formula for the triangle. The author also mentions how this pattern can be extended to higher dimensions using simplices.