How can Pfister's four-square identity be used to solve problems in number theory, such as finding representations of integers as sums of four squares

Question

Pfister's four-square identity is a theorem in number theory that states that the product of two numbers, each of which is a sum of four squares, is itself a sum of four squares. I'm interested in learning more about how this identity can be used to solve problems in number theory. For instance, are there any specific types of numbers that can be represented as sums of four squares in this way? Are there any specific types of integers that are particularly amenable to this type of representation? Can the identity be used to solve other types of problems in number theory as well? I would greatly appreciate any insights or references on this topic.