/usr/local/cpanel/log/error_log
cpanel logs any error it incurs here.This should be the first place you look when you encounter or strange behaviour in cpanel/ whm.
/usr/local/cpanel/logs/license_log
All license updates are logged here.if you run in any license errors when logging here, check here.
/usr/local/cpanel/log/stats_log
The stats daemon logs the output from all stats generator. (webalizer, bandwidth usage)
/usr/local/cpanel/logs/access_log
General information pertaining to cpanel request is logged here, (client information, request url)