If the cube is cut into 64 equal pieces one side may be of 4 unit. when we remove 1 unit from each from each sides i.e. the outer layer cubes ,the remaining cube will be of length 2 units. This cube is completely unpainted. Therefore the volume of the unpainted is 2x2x2. i.e.8 So the no. of unpainted cubes is 8.

Problem Statement:
A solid cube of 24cm has been painted black on one pair of opposite faces. The rest of the faces are painted blue. It is then cut into cubical blocks of side 4cm each. We need to determine how many cubes have at least one face painted blue.

Given:
- Solid cube side length: 24cm
- One pair of opposite faces painted black
- Rest of the faces painted blue
- Cubical blocks side length: 4cm

Solution:

Step 1: Determine the total number of cubes
The given solid cube has a side length of 24cm. Since we need to cut it into smaller cubes with a side length of 4cm, we can divide the side length of the large cube by the side length of the small cube to find the total number of cubes.

Total number of cubes = (Side length of large cube / Side length of small cube)^3
Total number of cubes = (24cm / 4cm)^3
Total number of cubes = 6^3
Total number of cubes = 216 cubes

Step 2: Identify cubes with at least one face painted blue
Since the large cube has one pair of opposite faces painted black, all the cubes that were part of those faces will have at least one face painted blue.

Step 3: Calculate the number of cubes with at least one face painted blue
The large cube has dimensions of 24cm x 24cm x 24cm. The opposite faces that are painted black have dimensions of 24cm x 24cm. Since we are cutting the large cube into smaller cubes with a side length of 4cm, we can calculate the number of cubes with at least one face painted blue on the opposite faces.

Number of cubes on opposite faces = (Side length of large cube / Side length of small cube)^2
Number of cubes on opposite faces = (24cm / 4cm)^2
Number of cubes on opposite faces = 6^2
Number of cubes on opposite faces = 36 cubes

Step 4: Calculate the number of cubes with at least one face painted blue on the other faces
The remaining faces of the large cube have dimensions of 24cm x 24cm x 16cm. Since we are cutting the large cube into smaller cubes with a side length of 4cm, we can calculate the number of cubes with at least one face painted blue on these faces.

Number of cubes on other faces = (Side length of large cube / Side length of small cube)^2 x (Height of large cube / Side length of small cube)
Number of cubes on other faces = (24cm / 4cm)^2 x (16cm / 4cm)
Number of cubes on other faces = 6^2 x 4
Number of cubes on other faces = 144 cubes

Step 5: Calculate the total number of cubes with at least one face painted blue
To find the total number of cubes with at least one face painted blue, we need to sum the cubes on the opposite faces and the other faces.

Total number of cubes with at least one face painted blue = Number of cubes on opposite faces + Number of cubes on other faces
Total number of cubes with at least

16