[number-sequence]

a rather interesting aspect of the taxicab number story is that ramanujan had been looking at "near misses" to the fermat equation, and this was the first values of one of the infinite families of near misses he had constructed. The story is often dramatized to make it sound like Ramanujan just knew about all the cubes and their sums and he pulled this out of thin air on the spot, but the truth is probably that he had worked enough with these equations to recognize the number when Hardy mentioned it.

check it out, super neat number thy stuff! https://arxiv.org/abs/1510.00735