Figure, 17 August 2017 · Mikko Kotila

1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15², and 15 = 1 + 2 + 3 + 4 + 5.

Each cube, cut into its layers, makes an L around the cubes before it, so that 1³ + 2³ + … + n³ = (1 + 2 + … + n)².