An a × b × c cuboid is constructed out of abc identical unit cubes -- a la Rubik's Cube.  Divide the cubes into two mutually exclusive types.  External cubes are those that constitute the faces of the cuboid; internal cubes are completely enclosed.  For example, the cuboid below has 74 external and 10 internal cubes.

Example cuboid: 3 by 4 by 7

Find all cuboids such that the number of external cubes equals the number of internal cubes.  (That is, give the dimensions of all such cuboids.)

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