There is no clustering of the solutions of $a^2+b^2+c^2=n$, even for individual $n$'s, assuming the number of solutions is large (e.g. when $n\equiv 1\pmod{4}$ and $n$ is large). This was proved by William Duke (Invent. Math. 92 (1988), 73-90), his paper is available (for free) [here][1]. 

For more recent results, e.g. what happens beyond equidistribution, see the work of Bourgain-Sarnak-Rudnick [here][2] and [here][3].


  [1]: http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002105063
  [2]: https://arxiv.org/abs/1204.0134
  [3]: https://arxiv.org/abs/1606.05880