Given a large number, <code data-no-translation=””>n, find all positive numbers less than or equal to <code data-no-translation=””>n that can be represented as the sum of two cubes for at least two different pairs.

In other words, find all positive numbers <code data-no-translation=””>m <= n that can be expressed as:

<code data-no-translation=””>m = (a³ + b³) = (c³ + d³) for distinct <code data-no-translation=””>a, <code data-no-translation=””>b, <code data-no-translation=””>c, <code data-no-translation=””>d.

For example,

If <code data-no-translation=””>n = 25000, <code data-no-translation=””>m can be any of <code data-no-translation=””>1729, <code data-no-translation=””>4104, <code data-no-translation=””>13832, or <code data-no-translation=””>20683 as these numbers can be represented as the sum of two cubes for two different pairs.

1729 = 1³ + 12³ = 9³ + 10³
4104 = 2³ + 16³ = 9³ + 15³
13832 = 2³ + 24³ = 18³ + 20³
20683 = 10³ + 27³ = 19³ + 24³

1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways.