# Ramanujan can do this instantly

Sunday, December 22 will be Srinivasa Ramanujan's $$126$$th birthday. Ramanujan was an amazing mathematician, but one of the things he was most famous for had to do with the number $$1729$$. When Ramanujan was in the hospital, he was visited by his friend G.H. Hardy. Hardy remarked that the taxicab that he had ridden in had a rather uninteresting number: $$1729$$. Ramanujan said that no, $$1729$$ was very interesting because it was the smallest number that can be expressed as the sum of $$2$$ cubes in $$2$$ different ways. These are $$12^3+1^3$$ and $$10^3+9^3$$. Hence, numbers that can be written as the sum of multiple cubes are called taxicab numbers.

In the spirit of the sums of cubes, $$126$$ can be written as the sum of two positive cubes, $$A^3$$ and $$B^3$$. What is $$A + B$$?

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