For any positive integer n, what is the greatest common divisor of all numbers in the form of "the third power of N + 3 times of n square + 2 times of n"

For any positive integer n, what is the greatest common divisor of all numbers in the form of "the third power of N + 3 times of n square + 2 times of n"

N ^ 3 + n ^ 2 + 2n ^ 2 + 2n
=n^2(n+1)+2n(n+1)
=n(n+1)(n+2)
That is, the product of three consecutive positive integers