For n=4 the cuboids are: 
3 X 7 X 43 X 1806, 
3 X 7 X 44 X 924, 
3 X 7 X 45 X 630, 
3 X 7 X 46 X 483, 
3 X 7 X 48 X 336, 
3 X 7 X 49 X 294, 
3 X 7 X 51 X 238, 
3 X 7 X 54 X 189, 
3 X 7 X 56 X 168, 
3 X 7 X 60 X 140, 
3 X 7 X 63 X 126, 
3 X 7 X 70 X 105, 
3 X 7 X 78 X 91, 
3 X 7 X 84 X 84, 
3 X 8 X 25 X 600, 
3 X 8 X 26 X 312, 
3 X 8 X 27 X 216, 
3 X 8 X 28 X 168, 
3 X 8 X 30 X 120, 
3 X 8 X 32 X 96, 
3 X 8 X 33 X 88, 
3 X 8 X 36 X 72, 
3 X 8 X 40 X 60, 
3 X 8 X 42 X 56, 
3 X 8 X 48 X 48, 
3 X 9 X 19 X 342, 
3 X 9 X 20 X 180, 
3 X 9 X 21 X 126, 
3 X 9 X 22 X 99, 
3 X 9 X 24 X 72, 
3 X 9 X 27 X 54, 
3 X 9 X 30 X 45, 
3 X 9 X 36 X 36, 
3 X 10 X 16 X 240, 
3 X 10 X 18 X 90, 
3 X 10 X 20 X 60, 
3 X 10 X 24 X 40, 
3 X 10 X 30 X 30, 
3 X 11 X 14 X 231, 
3 X 11 X 15 X 110, 
3 X 11 X 22 X 33, 
3 X 12 X 13 X 156, 
3 X 12 X 14 X 84, 
3 X 12 X 15 X 60, 
3 X 12 X 16 X 48, 
3 X 12 X 18 X 36, 
3 X 12 X 20 X 30, 
3 X 12 X 21 X 28, 
3 X 12 X 24 X 24, 
3 X 13 X 13 X 78, 
3 X 14 X 14 X 42, 
3 X 14 X 15 X 35, 
3 X 14 X 21 X 21, 
3 X 15 X 15 X 30, 
3 X 15 X 20 X 20, 
3 X 16 X 16 X 24, 
3 X 18 X 18 X 18, 
4 X 5 X 21 X 420, 
4 X 5 X 22 X 220, 
4 X 5 X 24 X 120, 
4 X 5 X 25 X 100, 
4 X 5 X 28 X 70, 
4 X 5 X 30 X 60, 
4 X 5 X 36 X 45, 
4 X 5 X 40 X 40, 
4 X 6 X 13 X 156, 
4 X 6 X 14 X 84, 
4 X 6 X 15 X 60, 
4 X 6 X 16 X 48, 
4 X 6 X 18 X 36, 
4 X 6 X 20 X 30, 
4 X 6 X 21 X 28, 
4 X 6 X 24 X 24, 
4 X 7 X 10 X 140, 
4 X 7 X 12 X 42, 
4 X 7 X 14 X 28, 
4 X 8 X 9 X 72, 
4 X 8 X 10 X 40, 
4 X 8 X 12 X 24, 
4 X 8 X 16 X 16, 
4 X 9 X 9 X 36, 
4 X 9 X 12 X 18, 
4 X 10 X 10 X 20, 
4 X 10 X 12 X 15, 
4 X 12 X 12 X 12, 
5 X 5 X 11 X 110, 
5 X 5 X 12 X 60, 
5 X 5 X 14 X 35, 
5 X 5 X 15 X 30, 
5 X 5 X 20 X 20, 
5 X 6 X 8 X 120, 
5 X 6 X 9 X 45, 
5 X 6 X 10 X 30, 
5 X 6 X 12 X 20, 
5 X 6 X 15 X 15, 
5 X 7 X 7 X 70, 
5 X 8 X 8 X 20, 
5 X 10 X 10 X 10, 
6 X 6 X 7 X 42, 
6 X 6 X 8 X 24, 
6 X 6 X 9 X 18, 
6 X 6 X 10 X 15, 
6 X 6 X 12 X 12, 
6 X 7 X 7 X 21, 
6 X 8 X 8 X 12, 
6 X 9 X 9 X 9, 
7 X 7 X 7 X 14, 
8 X 8 X 8 X 8.