Any rational number is a sum of three rational cubes.
First proved by Ryley in 1825, which can be found in [Ri1930].
The below parametrization is brought from the MSE answer [MSE].
[Ri1930] Richmond, H. W. "On Rational Solutions of $x^3 + y^3 + z^3 = R$." Proceedings of the Edinburgh Mathematical Society 2.2 (1930): 92-100.
[MSE] Kieren MacMillan, Proving that any rational number can be represented as the sum of the cubes of three rational numbers, https://math.stackexchange.com/q/4480969
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