Below is a list of paths for cPanel log files.
Logs in the /var/cpanel/:
/var/cpanel/horde/log/ (Horde)
/var/cpanel/roundcube/log/ (RoundCube)
/var/cpanel/squirrelmail/ (SquirrelMail)
/var/cpanel/logs (different cPanel logs)
/var/cpanel/accounting.log (creation, deletion of accounts, etc.)
/var/cpanel/bandwidth.cache/{USERNAME} (Per account bandwidth history (Cached))
/var/cpanel/bandwidth/{USERNAME} (Per account bandwidth history (Human Readable))
/var/cpanel/updatelogs/updated.DATE.log (update logs)
Logs in the /usr/local/cpanel/logs/:
/usr/local/cpanel/logs/access_log (user access and action logs)
/usr/local/cpanel/logs/cpbackup (backup)
/usr/local/cpanel/logs/cphulkd.log (cPHulk Protection)
/usr/local/cpanel/logs/dnsadmin_log (dnsadmin)
/usr/local/cpanel/logs/error_log (cPanel errors)
/usr/local/cpanel/logs/license_log (Licenses)
/usr/local/cpanel/logs/build_locale_database_log
/usr/local/cpanel/logs/login_log (Login errors)
/usr/local/cpanel/logs/panic_log (Errors)
/usr/local/cpanel/logs/tailwatch_log (Tailwatch)
/usr/local/cpanel/logs/updated_analysis/{TIMESTAMP}.log
/usr/local/cpanel/logs/cpdavd_error_log (WebDisk)
/usr/local/cpanel/3rdparty/mailmain/logs (Mailman)
/usr/local/cpanel/logs/queueprocd.log
/usr/local/cpanel/logs/setupdbmap_log
/usr/local/cpanel/logs/easy/apache/
/usr/local/cpanel/logs/splitlogs_log
/usr/local/cpanel/logs/stats_log
/usr/local/cpanel/logs/safeapcherestart_log
Logs in the /var/log/:
/var/log/cpanel (cPanel installation logs)
/var/log/cpanel-install.log
/var/log/chkservd.log (service status)
/var/log/maillog (mail logs)
/var/log/messages (mail logs)
/var/log/exim_rejectlog
/var/log/exim_paniclog (mail logs with errors)
/var/log/exim_mainlog (mail logs about delivery and receipt)
/var/log/slowqueries (a log of slow MySQL queries, if they are enabled in my.cnf)
/var/log/easy-tomcat7/localhost-access_log
/var/log/easy-tomcat7/catalina.err
/var/log/easy-tomcat7/catalina.out
Logs in other directories:
/usr/local/apache/domlogs/DOMAIN
/usr/local/apache/logs/suphp_log (suPHP)
/usr/local/apache/logs/error_log (web server errors)
/usr/local/apache/domlogs/ftpxferlog (FTP)
/home/user/logs/ (FTP and HTTP logs)
/var/spool/exim/input/ (incoming mail queue)
/var/lib/mysql/SERVER_NAME.err (MySQL Errors)
See also my article:
Location of configuration files cPanel & WHM