Common factors between two sequences

Let G(a, b) be the smallest non-negative integer n for which gcd(n³ + b, (n + a)³ + b) is maximized. For example, G(1, 1) = 5 because gcd(n³ + 1, (n + 1)³ + 1) reaches its maximum value of 7 for n = 5, and is smaller for 0 ≤ n < 5. Let H(m, n) = Σ G(a, b) for 1 ≤ a ≤ m, 1 ≤ b ≤ n. You are given H(5, 5) = 128878 and H(10, 10) = 32936544.

Find H(18, 1900).

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