Depth: 2
Cubes now: 400
Formula: 20ⁿ
Of 27 kept: 8 corners + 12 edges = 20

Fractal dimension: ln20/ln3 ≈ 2.727 — something between a flat surface (2D) and a solid body (3D): infinitely perforated, yet an infinitely detailed surface.

At each level a cube is cut into 27 sub-cubes (3×3×3); the center and the 6 face-centers (7 of 27) are removed — leaving 20 corner/edge sub-cubes, and the process repeats recursively in each of them.