Powers of numbers are a bit strange. 2^3 = 8, (2+1)^2 = 8+1. 3^7 = 2187, (3+10)^3 = 2187 + 10.

Are there any other cases of (n + m)^k = n^k' + m (where n, m, k, and k' are all positive integers. No zero because that means trivial solution, no k = 1 either.)