Can a CD disk and the memory of a device have an infinite space storage?
This is impossible.

Storing information requires physical space and there is a limit. This might seem somewhat obscured by the fact that we can store a lot of information in a small space, by the technological process which brought us smaller and smaller storage devices and by other factors which make the relationship between information and space less clear (e.g. a 700MB CD and a 50GB Blu-Ray disk have the same volume).

The limit on how much information can be stored is given by the Bekenstein bound:

$I \le \frac{2 \pi c R m}{\hbar ln2} $

$I$ is the information quantity that can be stored in a sphere with radius $R$ and mass $m$.

In short, you need an infinite amount of space to store an infinite amount of information, but a CD has a finite volume.