There have been many results about the number of squares needed to represent a positive integer. Lagrange's four-square theorem tells us that $4$ squares suffice for any integer and there have been results showing when you can do better than that.
What I'm interested in is why people consider these results interesting.
I can think of one interesting question that relates to these results. If we are allowed to construct lengths by drawing lines with integer lengths and making right-angled triangles out of them to construct new lengths the above theorem tells us that it is always possible to construct a line of length $\sqrt n$ (for any natural number $n$) and it is always possible to do that in at most $4$ "steps".
But beyond that this strikes me as a pretty random result. I'd therefore be interested in additional motivations for this result - historic or modern.