The cube, 41063625=(345)^3 can be permuted to produce two other cubes:
56623104=(384)^3 and 66430125=(405)^3.
In fact, 41063625 is the smallest cube for which exactly three permutations of its digits also form cubes.

Find the smallest cube for which exactly five permutations of its digits form cubes. (Project Euler, problem 62)

127035954683, with the rest of the set being:
352045367981
373559126408
569310543872
589323567104

Method: I made a listing all cubes of length n
and then inventoried their digits. E.g., the set
above for digits 987654321 inventories as 1111212111. I numerically sorted the inventories to find a stretch of 5 in a row. This happens only twice for the 12-digit cubes.

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