Applying the Ratio test, compute

 $\underset{n\to \infty }{lim}\frac{a_{n\+1}}{a_n}\=\underset{n\to \infty }{lim}\frac{\left(\frac{{\left(n\+1\right)}^3-1}{\left(n\+1\right)\!}\right)}{\left(\frac{n^3-1}{n\!}\right)}\=\underset{n\to \infty }{lim}\frac{n\left(n^2\+3n\+3\right)}{\left(n\+1\right)\left(n^3-1\right)}\=0$ 

from which it follows that the given series converges absolutely.

The most efficient way to implement the Ratio test in Maple, is to define the general term $a_n$ as a function $a\left(n\right)$.

This is series that Maple can sum exactly, and that also establishes its absolute convergence, provided the evidence of a computer computation is taken as sufficient mathematical proof.