Explanation:

- The problem is about finding relationships between numbers through cubes.

- The number 125 is related to 343. 125 is the cube of 5 ($5^3$) and 343 is the cube of 7 ($7^3$).

- Similarly, we must find a number related to 1331. 1331 is the cube of 11 (${11}^3$).

- The pattern suggests that if one number is the cube of 'x', the related number is the cube of 'x+2'.

- Therefore, the related number to 1331 should be the cube of 13 (${13}^3$).

- Option 4: 2197 is the cube of 13 (${13}^3$), thus the correct answer.

Therefore, the correct option is:

- Option 4: 2197