The name is attributed to a historical discussion between Ramanujan and G.H Hardy.
"I remember once going to see him when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways."
1729 is the smallest Taxicab Ta(2) number and can be expresses as cubes of 2 different sets of numbers (12, 1) and (10, 9).
A Python program for generating such numbers placing range conditions on a,b,c, and d yielded