Did you know that cPanel actually designed to be able to disallow certain folder/files to be backed up from your cPanel backup?
To accomplished this, you may look for the configuration file name cpbackup-exclude.conf. This configuration file exists in your virtual account root folder such as /home/username/cpbackup-exclude.conf.
If this file is not exist, you may simply create it.
Then you may open this file and enter the desired folder/files. The file format could be as below,
*/.wysiwygPro_* */core.[0-9] */core.[0-9][0-9] .MirrorSearch .cpan< .cpanel/caches .cpanel/datastore .cpcpan .wysiwygPro_* access-logs core.[0-9] core.[0-9][0-9] public_ftp/.ftpquota