Diophantines

There are some triples of positive integers such that the sum of their cubes is also a perfect cube, for example

$1^{3}+6^{3}+8^{3}=9^{3}$ or $3^{3}+10^{3}+18^{3}=19^{3}$ .

Find the possible values of n where there exists n-tuples

$a_{1},a_{2}, ... ,a_{n}$ where the equation $a_{1}^{3}+a_{2}^{3}+ ... +a_{n}^{3}=b^{3}$ holds.

Note: The answer selections may not contain all possible values of n.