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problem 62 · 4 lines

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<p>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 which has exactly three permutations of its digits which are also cube.</p>
<p>Find the smallest cube for which exactly five permutations of its digits are cube.</p>
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