Let $n$ be a positive integer and $p$ a prime number. I know that there are formulas by which one can compute the number of representations of $n$ as the sum of two or three squares etc.

I would to know if there is a formula describing the number of representations of $n$ as the following form $a^{2}+b^{2}+p^{2}c^{2}$, $a,b, c\in\mathbb{N}$.

Thank you.