What is the largest integer with only one representation as a sum of five nonzero squares? It seems to be very well known that $33$ is the largest integer with zero representations as a sum of five nonzero squares. So it seems reasonable to me that as we go higher and higher, numbers have more and more representations as sums of five nonzero squares, and maybe there is a threshold above which all numbers have at least two such representations.
My question is, what is the largest integer with only one representation as a sum of five nonzero squares?

You may find it interesting to have a glance at this image: http://oeis.org/A025429/graph (Number of partitions of n into 5 nonzero squares).
 -- see also http://oeis.org/A080673 = largest numbers with exactly n representations as sum of five positive squares. 
