N unit cubes are assembled to form a larger cube (N is a positive integer.)

In the larger cube thus assembled, some of the faces are then painted.

The cube is now taken apart and it is found that 271 of the unit cubes have paint on them.

Find N.

(In reply to Considering all the possibilities by Charlie)

I was thinking of some follow-up questions to this, but all of them are easily answered by inspection of this nice chart.

Posted by Jer on 2016-09-29 07:27:30