A BDMO functional equation problem.
Choosing $y=-x$, we have that $2f(x^2) = f(f(0))$, in other words $f$ is constant on square numbers. From the initial condition we can deduce a bunch of things, one of them is that $f(1010^2) = 505$. So $505$ is the value on all squares, including $f(2025) = f(45^2)$.