We can manually upgrade  the exim mail server latest version using cpanel scripts the name of "eximup" its being under the directory /scripts

Login into your server with super user using ssh and run the eximup script,

# /scripts/eximup

After updated exim mail server check the latest version using below command,
linux@host# exim -bV
Exim version 4.82 #2 built 08-Nov-2013 14:10:25
Copyright (c) University of Cambridge, 1995 - 2013
Configuration file is /etc/exim.conf

If you want to see the latest version in future, can download the exim mail server package from below link with any version,