The correct answer is Option A: 8.
To solve this problem, we need to determine how many of the smaller 1 cm x 1 cm x 1 cm cubes do not have any painted faces after the larger cube is sliced.
     Step-by-step Explanation:
     1. Understanding the Cube Structure:
            ○ The original cube is a 4 cm x 4 cm x 4 cm cube.
            ○ It is sliced into 64 smaller cubes, each measuring 1 cm x 1 cm x 1 cm.
     2. Identifying the Inner Cubes:
            ○ The outer layer of the cube is painted, which means all cubes on the surface have at least one face painted.
            ○ To find the cubes that do not have any painted faces, we need to focus on the inner cubes that are not exposed to the surface.
     3. Calculating the Inner Layer:
            ○ The inner cubes form a smaller cube inside the original cube.
            ○ This inner cube is formed by removing the outer layer of 1 cm thickness from each face of the original cube.
            ○ The dimensions of the inner cube are (4 - 2) cm x (4 - 2) cm x (4 - 2) cm = 2 cm x 2 cm x 2 cm.
     4. Counting the Inner Cubes:
            ○ The inner cube is composed of 2 x 2 x 2 = 8 smaller cubes.
     Therefore, there are 8 small cubes that do not have any painted faces. These are the cubes located entirely within the inner 2 cm x 2 cm x 2 cm cube.
     Hence, the correct answer is Option A: 8.