Find the Largest Cube formed by deleting minimum number of digits from a number

Given a number N, our task is to find the largest perfect cube that can be formed by deleting minimum digits (possibly 0) from the number. Any digit can be removed from the given number to reach the goal.


This is a companion discussion topic for the original entry at http://iq.opengenus.org/find-the-largest-cube-formed-by-deleting-minimum-digits-from-a-number/