Found a very interesting method to find cube roots may be this will be useful.
With them you can find any two-digit cube root. For example, what's the cube root of 12,167?
1. Express the number in six digits (012167). Take the first three digits (012) and compare them to the blue cubes above. Find the largest cube that's less than your three-digit string, and write down its root. Here, 012 is between 8 and 27, so we write down 2.
2. Match the last digit of the number (7) to the last digit of a blue cube above (here, 27). Write down the root of that number (3).
That's it. Put the two digits together (23) and that's your root: 233 = 12,167.
This works for any perfect cube between 1,000 and 1 million.