Sum of cubes of first n natural numbers = $[\dfrac{n(n + 1)}{2}]^{2}$
Here the sum of cubes is a perfect square of some number. Figure out if any of the options is not a perfect square. That will be the answer.
1 is a perfect square [Eliminate]
23409 is a perfect square [Eliminate]
8521 is not a perfect square [= Answer]