MathNet 2007-part-03 — 185 problems (EN–VI) Question 9

Let $a_{n}=1+n^{3}$ be the sequence $\{2,9,28,65, \ldots\}$ and $\delta_{n}=\gcd\left(a_{n+1}, a_{n}\right)$. Find the maximum value that $\delta_{n}$ can take.