I got this while solving this Problem: Three cubes and a square
I was working for the answer (laboriously). I then found one special cube number.
It was 216. That number can be expressed as the sum of three consecutive cubes;27, 64 and 125 surprisingly add up to the next cubic number.
I also saw that cube roots of the numbers are in the Pythagorean Triples (3,4,5). However, Pythagorean triples are self-contained but these cubes have the sum of an external cube. The question is : Is there another number that has this property?
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There is a formula by Ramanujan to generate cubes that are the sum of three other cubes.
I found it here.
There's also
From here
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Thank you, Henry