I found this here:
Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same.
Here is one of 20 736 solutions with the sum 14.
You find more at the German magazine "Bild der Wissenschaft 3-1980".
Now my question:
Is $14$ the only possible face sum? At least, in the example given, it seems to related to the fact, that on every face two dice-pairs show up, having $n$ and $7-n$ pips. Is this necessary? Sufficient it is...