First check contents of your files in /mail/new to make sure there is no important mail.
On my cPanel account i have no email account set so when my website send an email to mailbox that dont exist or any other error, the mail is returned there into /mail/new filling space of my hosting account.
So i decided to automatically delete all this mail instead of saving it in /mail/new .
How to automatically delete unrouted emails in cPanel?
There is how to set auto deleting of these emails from within cPanel:
cPanel / Default Address / Advanced Options » / select "Discard (Not Recommended)" / Change
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