Ramanujan can do this instantlyNumber Theory Level 1
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 \( A + B \)?