What number can you cube to make it bigger than 200 but smaller than 400

If you would like to cube one number and make it bigger than 200 but smaller than 400, you can find the number using the following steps:

n ... the number
200 < n^3 < 400

For example: 
If n equals to 6, then n^3 = 6^3 = 6 * 6 * 6 = 216 and 200 < 216 < 400, so the result could be 6.
If n equals to 7, then n^3 = 7^3 = 7 * 7 * 7 = 343 and 200 < 343 < 400, so the result could also be 7.
But, if n is 8, then n^3 = 8^3 = 8 * 8 * 8 = 512 and 512 > 400.

Result: You can take the numbers 6 and 7.