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Answer to puzzle 35: Cuboids

There are 20 distinct cuboids such that the number of external cubes is equal to the number of internal cubes.  The table below shows the dimensions (a × b × c) and number of external cubes for each such cuboid.

List of cuboids
abc# external cubes
5131324290
514722520
515521950
516421680
517361530
518321440
520271350
522241320
69561512
61032960
61124792
61220720
61416672
771002450
7830840
7920630
71016560
8818576
8914504
81012480