The perfect cube:
A perfect cube is a number that can be expressed as the cube of an integer. In other words, it is the result of multiplying an integer by itself twice.

Approach:
To determine which of the given options is a perfect cube, we need to find the cube root of each number and check if it is an integer. If the cube root is an integer, then the number is a perfect cube.

Solution:

Let's analyze each option one by one:

a) 441:
To find the cube root of 441, we need to find a number x such that x * x * x = 441. By checking different numbers, we find that the cube root of 441 is 7. Since the cube root is an integer, 441 is a perfect cube.

b) 514:
To find the cube root of 514, we need to find a number x such that x * x * x = 514. By checking different numbers, we find that the cube root of 514 is not an integer. Therefore, 514 is not a perfect cube.

c) 412:
To find the cube root of 412, we need to find a number x such that x * x * x = 412. By checking different numbers, we find that the cube root of 412 is not an integer. Therefore, 412 is not a perfect cube.

d) 343:
To find the cube root of 343, we need to find a number x such that x * x * x = 343. By checking different numbers, we find that the cube root of 343 is 7. Since the cube root is an integer, 343 is a perfect cube.

Conclusion:
Out of the given options, only 343 is a perfect cube. Therefore, the correct answer is option 'D'.