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I asked the question and can answer it for those interested. There is an infinite series of numbers of the order (a)3 + (b)3 = (c)3 +(d)3 as follows for a = 1,2,3... 1,729 = (1)3 + (12)3 = (9)3+ (10)3 13,832 = (2)3 + (24)3 = (18)3 + (20)3 46,683 = (3)3 + (36)3 = (27)3 + (30)3 . . . . . . . . . . . . . . .Also, I found others not in the series such as 134,379=(12)3+(51)3 = (38)3 +(43)3 and I am curious as to whether this is a known number set.

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Q: What numbers have two double sets of cube roots?
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