Subdomain for cloud hosting service

I'm using a cloud file hosting service that hosts my files at say "http://cf3hifif3445.example.domain.com/filename.ext" and I was wondering if there's a way to make it appear to the user as the files are coming from "http://files.mydomain.com/filename.ext"

Basically "http://files.mydomain.com" == "http://cf3hifif3445.example.domain.com"

Is this possible? If so, would it be a server thing or DNS or something else?

Forgot to add (if this matters):
I'm using CentOS with cPanel
And if this is the wrong forum, well...this is embarrassing

It is possible, but it needs to be set up on the hosting server, as well as your own DNS. Unless you have access to change the DNS settings in the cloud server, then you might be out of luck.

Thanks, after further investigating, it looks like I simply need to change CNAMES.