A number is called \mathit{good} if it can be written as the sum of the squares of three consecutive positive integers. A number is called \mathit{excellent} if it can be written as the sum of the squares of four consecutive positive integers. (For instance, 14 = 1^2 + 2^2 + 3^2 is good and 30 = 1^2 + 2^2 + 3^2 + 4^2 is excellent.) A good number G is called splendid if there exists an excellent number E such that 3G - E = 2025. If the sum of all splendid numbers is S, find the remainder when S is divided by 1000.