Is there a perfect square that is the sum of $3$ perfect squares? This is part of a bigger question, but it boils down to:
Is there a square number that is equal to the sum of three different square numbers?
I could only find a special case where two of the three are equal? https://pir2.forumeiros.com/t86615-soma-de-tres-quadrados (in portuguese).
Any clue?

There are infinitely many: for any positive integer $n$ we have
$$n^2(n+1)^2+n^2+(n+1)^2=(n(n+1)+1)^2$$
