Path to Palindromes

A number can be converted to a palindrome by summing the cube of each digit and repeating this procedure. For example; 36 converts to 99 in 2 steps. Likewise 17 converts to 737 in 6 steps. We assume a number is not convertible in this way if it does not reach a palindrome in at most 100 steps. Below one million, which number has to undergo most steps(if there are more than one, assume smallest). Give your answer as number.steps