This $4\times 4\times 4$ puzzle cube is made of small cubes and is seen from one corner, so three faces are visible. How many small cubes cannot be seen at all from this view?

For non-perfect cubes, bracket the cube root between two consecutive integers.

Example: ∛100. We know $4^3=64$ and $5^3=125$. So 4 < ∛100 < 5. Closer to 5 (100 is closer to 125 than 64). Refined estimate: ∛100 ≈ 4.64.

For perfect cubes, look at the last digit (last digit rule for cubes: each digit cubes to a unique last digit). 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0.