NOTE: By default, cPanel does not provide a method of downloading a zone file which contains the all the DNS Zones of the domains on a particular cPanel account. However the file does exist and there is a simple trick to find this file
Step 1 - You will need to use the cPanel Backup Wizard to make a Full Backup of your cPanel account (click here for a guide). Download the backup to your computer once it's complete.
Step 3 - In the extracted files, look for a folder titled dnszones and open it up
The list of files here are the zone files for each domain on that cPanel account. You can view them by opening the file with any text editor (Notepad, Microsoft Word, etc)