Option B: 24
To solve this problem, we need to understand the structure of the cube and how it is divided:
     1. Initial Setup:
            ○ We have a large cube with each face painted a different color.
            ○ The large cube is divided into smaller cubes, where the side of each small cube is one-fourth the side of the large cube.
     2. Division of the Cube:
            ○ Since the side of each small cube is one-fourth of the large cube, the large cube is divided into \(4 \times 4 \times 4 = 64\) smaller cubes.
     3. Identifying Small Cubes with One Painted Face:
            ○ Small cubes with only one face painted are located on the faces of the large cube but not on the edges or corners.
            ○ Each face of the large cube is a \(4 \times 4\) grid of small cubes.
            ○ The cubes on the edges and corners of each face will have more than one face painted.
     4. Counting the Small Cubes with One Painted Face:
            ○ On each face of the large cube, the inner \(2 \times 2\) grid of small cubes will have only one face painted.
            ○ This inner grid consists of \(2 \times 2 = 4\) small cubes per face.
     5. Total Calculation:
            ○ Since the large cube has 6 faces, and each face contributes 4 small cubes with only one face painted, the total number of such small cubes is:
          \[
          6 \times 4 = 24
          \]
     Therefore, the number of small cubes with only one of the sides painted is 24.