Each cube below is made up of smaller cubes, but the large cubes are not solid. They had tunnels through them.

• The first cube originally had 27 small cubes, but the tunnel removed 3 cubes.
• The second cube originally had 64 small cubes, but two straight tunnels, 4 cubes deep, removed some cubes.
• The third cube, which originally had 125 small cubes, has 3 straight tunnels, five cubes deep from face to face.
The outside surfaces of these cube constructions have been painted including inside the tunnels and on the bottom. For each construction, how many small cubes have paint on 4 faces? 3 faces? 2 faces? 1 face? 0 face?

To determine the number of small cubes with paint on each number of faces, we need to consider the effects of the tunnels for each cube construction.

For the first cube:
- The total number of small cubes is originally 27.
- However, 3 small cubes were removed due to the tunnel.
- Therefore, there are 24 small cubes remaining.
- Each small cube has 0 faces painted since the tunnels also removed paint from the inside.

For the second cube:
- The total number of small cubes is originally 64.
- Two straight tunnels, 4 cubes deep, were created.
- This means that a 4x4x4 cube in the center has been removed, leaving a 4x4x4 cube frame.
- The total number of small cubes remaining is (4x4x4) - (4x4) = 64 - 16 = 48.
- Each small cube on the outside surface of the frame has 3 painted faces.
- Each small cube on the inside surface of the frame has 2 painted faces.
- Each small cube on the edge of the frame (excluding corners) has 1 painted face.
- Each corner cube has 0 painted faces.

For the third cube:
- The total number of small cubes is originally 125.
- Three straight tunnels, five cubes deep, were created.
- This means that a 5x5x5 cube in the center has been removed, leaving a 5x5x5 cube frame.
- The total number of small cubes remaining is (5x5x5) - (5x5) = 125 - 25 = 100.
- Each small cube on the outside surface of the frame has 3 painted faces.
- Each small cube on the inside surface of the frame has 2 painted faces.
- Each small cube on the edge of the frame (excluding corners) has 1 painted face.
- Each corner cube has 0 painted faces.

Summary of the number of small cubes with paint on each number of faces:
1st Cube:
- 24 small cubes with 0 faces painted.

2nd Cube:
- 8 corner cubes with 0 faces painted.
- 16 edge cubes with 1 face painted.
- 24 inside surface cubes with 2 faces painted.
- 48 outside surface cubes with 3 faces painted.

3rd Cube:
- 8 corner cubes with 0 faces painted.
- 36 edge cubes with 1 face painted.
- 54 inside surface cubes with 2 faces painted.
- 100 outside surface cubes with 3 faces painted.

Note: It is important to double-check the cube configurations and tunnel positions to ensure accurate results.

To determine the number of small cubes that have paint on 4 faces, 3 faces, 2 faces, 1 face, and 0 faces for each construction, we need to analyze how the tunnels affect the larger cubes.

Let's start by calculating for the first cube:

1. The first cube originally had 27 small cubes.
2. The tunnel removed 3 cubes, leaving 24 small cubes.
3. For each of the 24 remaining small cubes, there will be 4 faces with paint.

So, for the first cube:
- Number of small cubes with paint on 4 faces: 24
- Number of small cubes with paint on 3 faces: 0
- Number of small cubes with paint on 2 faces: 0
- Number of small cubes with paint on 1 face: 0
- Number of small cubes with paint on 0 faces: 0

Next, let's move on to the second cube:

1. The second cube originally had 64 small cubes.
2. Two straight tunnels, 4 cubes deep, removed some cubes.
3. Since the tunnels are 4 cubes deep, they remove 4*2 = 8 cubes in total.
4. This leaves 64 - 8 = 56 small cubes remaining.
5. For each of the 56 remaining small cubes, there will be 3 faces with paint (since one face is shared with the removed cubes).

So, for the second cube:
- Number of small cubes with paint on 4 faces: 0
- Number of small cubes with paint on 3 faces: 56
- Number of small cubes with paint on 2 faces: 0
- Number of small cubes with paint on 1 face: 0
- Number of small cubes with paint on 0 faces: 0

Now, let's calculate for the third cube:

1. The third cube originally had 125 small cubes.
2. There are 3 straight tunnels, each five cubes deep from face to face.
3. Considering the depths of the tunnels, each tunnel removes 5*5 = 25 cubes.
4. So the total number of cubes removed by the tunnels is 25*3 = 75.
5. The remaining number of small cubes is 125 - 75 = 50.
6. For each of the 50 remaining small cubes, there will be 2 faces with paint (since two faces are shared with the removed cubes).

So, for the third cube:
- Number of small cubes with paint on 4 faces: 0
- Number of small cubes with paint on 3 faces: 0
- Number of small cubes with paint on 2 faces: 50
- Number of small cubes with paint on 1 face: 0
- Number of small cubes with paint on 0 faces: 0

To summarize, the number of small cubes with paint on each number of faces for each construction is as follows:

First Cube:
- 4 faces: 24 cubes
- 3 faces: 0 cubes
- 2 faces: 0 cubes
- 1 face: 0 cubes
- 0 faces: 0 cubes

Second Cube:
- 4 faces: 0 cubes
- 3 faces: 56 cubes
- 2 faces: 0 cubes
- 1 face: 0 cubes
- 0 faces: 0 cubes

Third Cube:
- 4 faces: 0 cubes
- 3 faces: 0 cubes
- 2 faces: 50 cubes
- 1 face: 0 cubes
- 0 faces: 0 cubes