How many cubes have 2 painted faces?

A hard-level "Count" problem.For N×N×N: 3 faces is always 8, 2 faces is 12×(N−2), 1 face is 6×(N−2)², 0 faces is (N−2)³. They add up to exactly N³.

Given64 one-cm cubes make a 4 cm cube / all outside faces painted

Hints

Counting all 64 one by one is hard. Instead, sort them by how they are painted. Where a cube sits decides how many faces face outwards.
First the corners. There are 8 of them, and each has three faces outside (3 faces).
Next the middle of a face. Only one face is outside (1 face). There are 6 faces, each holding (4 − 2) × (4 − 2) = 4 cubes.
What is left are the cubes lined up along the edges. These are the "2 faces" group.
Each edge holds 4 cubes, but the two ends are corners with 3 faces. The 4 − 2 = 2 in the middle have 2 faces.
A cube has 12 edges, 2 each, so 12 × 2 = 24 cubes.
Let's check. 3 faces: 8; 2 faces: 24; 1 face: 24; hidden inside with no paint: 8. Total 64. It matches exactly. What was asked here is "2 faces" = the cubes on the edges (corners not counted).

Answer 24pcs