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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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