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)