"8 Dice arranged as a Cube" Face-Sum Equals 14 Problem I found this here:

Sum Problem
Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same.
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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...

No, 14 is not the only possibility.
For example:
Arrange the dice, so that you only see 1,2 and 3 pips and all the 2's are on the upper and lower face of the big cube. This gives you face sum 8.
Please ask your other questions as separate questions if you are still interested.
