15. The number $n^{k}$ for $k \geqslant 2$ is the sum of $n$ consecutive odd numbers.
15. $(2 a+1)+(2 a+3)+\ldots+(2 a+2 n-1)=n^{k}$, $(2 a+n) n=n^{k}, a=\frac{n^{k-1}-n}{2} ;$ for example, for $3^{5}$ we have: $a=$ $=\frac{3^{4}-3}{2}=39 ; 3^{5}=79+81+83$.