The number of representations is calculated by N. Bagis and M.L Glasser in <A HREF="http://arxiv.org/abs/1406.0466">On the Number of Representations of Integers by various Quadratic and Higher Forms</A> (2014):

<IMG SRC="http://ilorentz.org/beenakker/MO/sumofsquares_2.png"/>

where $r(n)$ is Jacobi's formula for the number of representations of $n=x^2+y^2$.