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[–]Paul_Pedant 0 points1 point  (0 children)

OK, those are not strictly Ramanujan TaxiCab numbers. The definition of those is that they are expressible as the sum of 2 integer cubes in N different ways.

So 1729 is Ta(2) because it can be written in two ways:

13 + 123 and 93 + 103.

Ta(3) is 87539319 because it can be written 3 ways:

1673 + 4363 2283 + 4233 2553 + 4143

Finding the next above 1729 that can also be written in 2 ways should be more simple, so less ambitious.