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It may be simpler to focus on just three faces (the three different faces), rather than on all six.
This net of a cuboid may help.
Try to be systematic:
if the height is $1$, what are the possible combinations for the width and depth?
if the height is $2, 3, 4$... what are the possible combinations for the width and depth?
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?