I find 25 a very soothing square number. Maybe one reason is that 5 is so squarely in the middle of the 1-10 range, so 25 doesn't feel like it wants to be rounded up or down. It is very solidly where it is and it isn't going to wobble. And perhaps partly because it feels pretty obvious that 25 is a square of 5. The 5 is right in there. At the end, like a surname. "Twenty Five, heir to the Five manor."
Do you have a favorite square number? For fanciful reasons?