There are bound to be multiple solutions to your problem. I would suggest that you add a few constraints to your problem.
I would consider the idea that a cube fits exactly x^x cubes if you are putting cubes of size 1/x relative to the cube. So as an example you have 1,4,27, different cubes for x = 1,2,3.
If you can solve for the number of cubes to be 2014 then you are done. This means that you are summing each set of cubes in a hierarchical manner. You can look at the problem by solving the equation:
a*1 + b*2^2 + c*3^3 + d*4^4 + .... + = 2014 where you limit the terms to the appropriate size (i.e. x^x < 2014).
Hopefully that will get you started.