MathDB

A large cube of size

4 \times 4 \times 4

is made up of 64 small unit cubes. Exactly 16 of these small cubes must be colored red, subject to the following condition:
In each block of

1 \times 1 \times 4

1 \times 4 \times 1

, and

4 \times 1 \times 1

cubes, there must be exactly one red cube.
Determine how many different ways it is possible to choose the 16 small cubes to be colored red.
Note: Two colorings are considered different even if one can be obtained from the other by rotations or symmetries of the cube.

Problem Statement