Given a cube with dimensions 4 cm × 4 cm × 4 cm, it is sliced into 64 smaller cubes, each of size 1 cm × 1 cm × 1 cm. We are asked to find how many of these smaller cubes do not have painted faces.

1. Total number of smaller cubes: The cube is divided into smaller cubes of size 1 cm × 1 cm × 1 cm. The total number of smaller cubes is given by: $4 \times 4 \times 4 = 64$ small cubes.

2. Cubes with painted faces: The painted cubes are those on the outer surface of the large cube. These are the cubes that lie on the faces of the large cube.

3. Unpainted cubes: The unpainted cubes are those that are entirely inside the large cube, away from the faces. These cubes form a smaller cube with side length 2 cm in the center of the original cube. The dimensions of this smaller cube are: $2 \times 2 \times 2 = 8$ unpainted cubes.

Thus, the number of small cubes that do not have painted faces is 8.

Answer: A. 8