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.