(x^2+y^2)/2 where x and y have the same parity. will it result a sum of 2 perfect squares

in other words

x^2 + y^2 =2 (a^2 +b^2) and x^2 + y^2 is even

the solution becomes obvious if you realize that

(a+b)^2 + (a-b)^2 = 2(a^2+b^2)

so x = a+b and y = a- b is a solution and both a and b should be even or odd