Its very easy question really.You can empty cPanel servers logs by using following commands
Login into server as root
root@gunjan[#]vi logs
echo > /usr/local/apache/logs/error_log
echo > /usr/local/apache/logs/access_log
echo > /usr/local/apache/logs/access_log
echo > /usr/local/apache/logs/error_log
echo > /usr/local/cpanel/logs/access_log
echo > /usr/local/cpanel/logs/error_log
echo > /var/log/exim_mainlog
echo > /var/log/exim_rejectlog
echo > /var/log/maillog
echo > /var/log/messages
echo > /var/log/messages.1
echo > /var/log/maillog.1
:wq!
root@gunjan[#]chmod 755 logs
root@gunjan[#]./logs
It will empty all logs present on your server.
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