Math Brain Teaser involving patterns and numbers?

To begin with the question/example is flawed... would it not be 4^4+3^3+3^3? There are other numbers, and you can discover ALL of them if you can write the algorithm. But if you are satisfied with one or two more, it is a simple algebraic equation. Or, if you want to do it quickly with calculus, just find (manually) a couple of examples which come 'close' to working (like 32 or 3151), then as you change the variables, the derivative will be your answer. Example: (6^6/((3^3)/(3^3))((/2^2)/2^2))=2^2)