Arithmetic functions commutable with sums of squares

In this note, we characterize all functions $f : $\mathbb{N}$ \rightarrow $\mathbb{C}$$suchthat$f(x_1^2+ \cdots + x_k^2)=f(x_1)^2+ \cdots + f(x_k)^2$, where $k\ge 3$ and $x_1,\cdots ,x_k$ are positive integers.