Cyclic group of prime-cube order

Definition
Let $$p$$ be a prime number. The cyclic group of order $$p^3$$ is a cyclic group (specifically, a finite cyclic group whose order is $$p^3$$. It can be defined by the presentation:

$$\langle a \mid a^{p^3} = e \rangle$$

where $$e$$ is the identity element. The group is written $$\mathbb{Z}_{p^3}, C_{p^3}$$ or $$\mathbb{Z}/p^3\mathbb{Z}$$.

Alternative descriptions
The group can be described using GAP's CyclicGroup function:

CyclicGroup(p^3)

where we can replace $$p$$ by a particular prime or replace $$p^3$$ by a particular cube of a prime.