Cube of 3

3 cubed equals 27. Cubes show up in volume calculations — a cube with side 3 holds 27 cubic units.

Cubes carry the fingerprint of their base. The final digit of 27 is 7 — always the cube of the base's own final digit. Divided by 9, a cube only ever leaves 0, 1 or 8, and 27 leaves 0. The volume picture explains the name: a 3 × 3 floor of unit cubes holds 9 of them, and 3 such layers stack to 27 — the shape itself is the exponent at work. The gaps grow like a parabola: 27 − 8 = 19, which is 3 × 3 × 2 + 1 — each new layer wider than the last. Odd base, odd cube: 27 stays odd, as 3 is.