Pandigital Puzzle

Question

Can you find the 10 digit number* which contains each of the digits 0-9* exactly once, and when divided by 9 the quotient is a perfect cube which has the digit 7 in it exactly twice*?

*in its base 10 representation

For clarification:

• 1014107283 does not qualify, since although 483³=112678587 has two 7s, when multiplied by 9 the product (1014107283) is missing digits 5, 6 and 9.
• 1963504872 does not qualify, since although 602³=218167208 and when multiplied by 9 the product 1963504872 is pandigital, 218167208 has only one 7.

Answer 1

It is

1905378624

which, divided by 9 gives

211708736

which contains two sevens and is the third power of

596