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Problem 62

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Cubic permutations

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.

Find the smallest cube for which exactly five permutations of its digits are cube.

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立方数重排

立方数$41063625$（$345^3$）可以重排为另外两个立方数：$56623104$（$384^3$）和$66430125$（$405^3$）。实际上，$41063625$是重排中恰好有三个立方数的最小立方数。

求重排中恰好有五个立方数的最小立方数。

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