1729 is called Ramanujan's number. Its famous because,
1729 = 1^3 + 12^3 = 9^3 + 10^3
The importance of this number first came through the conversation of two famous Mathematician Hardy and Ramanujan. I am quoting Hardy,
" I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."