A 4x4x4 solid can be filled with three copies of a pentacube and seven copies of a heptacube. Here we restrict the heptacube to be a solid heptomino.

Below is a catalog of the pentacube/heptomino pairs for which solutions exist. The catalog links to solution drawings whenever there are five or fewer solutions. For example, to see the two solutions for three U-pentacubes and three cleaver-heptacubes, click the solution drawings link. In the bottom half of the linked window you will see a frame for each solution. Within the frame you can click on the next (or previous) link to add (or remove) a piece from the drawing.
1: 3 P-pentacubes, 7 cobra-heptacubes
1 solution

7×
solution drawings
2: 3 P-pentacubes, 7 gun-heptacubes
1 solution

7×
solution drawings
3: 3 S-pentacubes, 7 cleaver-heptacubes
1 solution

7×
solution drawings
4: 3 W-pentacubes, 7 cleaver-heptacubes
1 solution

7×
solution drawings
5: 3 L3-pentacubes, 7 notch-heptacubes
1 solution

7×
solution drawings
6: 3 T2-pentacubes, 7 notch-heptacubes
1 solution

7×
solution drawings
7: 3 L1-pentacubes, 7 bulldozer-heptacubes
1 solution

7×
solution drawings
8: 3 L2-pentacubes, 7 bulldozer-heptacubes
1 solution

7×
solution drawings
9: 3 L2-pentacubes, 7 cleaver-heptacubes
1 solution

7×
solution drawings
10: 3 L4-pentacubes, 7 eff-heptacubes
1 solution

7×
solution drawings
11: 3 N2-pentacubes, 7 notch-heptacubes
1 solution

7×
solution drawings
12: 3 S-pentacubes, 7 notch-heptacubes
2 solutions

7×
solution drawings
13: 3 U-pentacubes, 7 cleaver-heptacubes
2 solutions

7×
solution drawings
14: 3 V-pentacubes, 7 notch-heptacubes
2 solutions

7×
solution drawings
15: 3 Z-pentacubes, 7 cleaver-heptacubes
2 solutions

7×
solution drawings
16: 3 T2-pentacubes, 7 bulldozer-heptacubes
2 solutions

7×
solution drawings
17: 3 L1-pentacubes, 7 notch-heptacubes
2 solutions

7×
solution drawings
18: 3 N2-pentacubes, 7 bulldozer-heptacubes
2 solutions

7×
solution drawings
19: 3 T-pentacubes, 7 cleaver-heptacubes
3 solutions

7×
solution drawings
20: 3 V-pentacubes, 7 cleaver-heptacubes
3 solutions

7×
solution drawings
21: 3 N1-pentacubes, 7 bulldozer-heptacubes
3 solutions

7×
solution drawings
22: 3 U-pentacubes, 7 notch-heptacubes
4 solutions

7×
solution drawings
23: 3 Y-pentacubes, 7 bulldozer-heptacubes
4 solutions

7×
solution drawings
24: 3 A-pentacubes, 7 notch-heptacubes
4 solutions

7×
solution drawings
25: 3 F-pentacubes, 7 notch-heptacubes
5 solutions

7×
solution drawings
26: 3 P-pentacubes, 7 jay-heptacubes
5 solutions

7×
solution drawings
27: 3 L3-pentacubes, 7 bulldozer-heptacubes
5 solutions

7×
solution drawings
28: 3 Y-pentacubes, 7 cleaver-heptacubes
6 solutions

7×
29: 3 L4-pentacubes, 7 notch-heptacubes
6 solutions

7×
30: 3 L-pentacubes, 7 gun-heptacubes
8 solutions

7×
31: 3 L4-pentacubes, 7 cleaver-heptacubes
8 solutions

7×
32: 3 L-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
33: 3 L-pentacubes, 7 cleaver-heptacubes
many solutions

7×
34: 3 L-pentacubes, 7 notch-heptacubes
many solutions

7×
35: 3 P-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
36: 3 P-pentacubes, 7 cleaver-heptacubes
many solutions

7×
37: 3 P-pentacubes, 7 notch-heptacubes
many solutions

7×
38: 3 S-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
39: 3 T-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
40: 3 U-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
41: 3 V-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
42: 3 Y-pentacubes, 7 notch-heptacubes
many solutions

7×
43: 3 L3-pentacubes, 7 cleaver-heptacubes
many solutions

7×
44: 3 Q-pentacubes, 7 bulldozer-heptacubes
many solutions

7×
45: 3 Q-pentacubes, 7 cleaver-heptacubes
many solutions

7×
46: 3 Q-pentacubes, 7 notch-heptacubes
many solutions

7×
47: 3 L4-pentacubes, 7 bulldozer-heptacubes
many solutions

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