Mysql CPU usage too high at same time daily

I have a big problem with my server. Every night at 2:00 AM is going down for 20-30 minutes. After many investigations mysql looks to be the problem.

I have :
CentOS release 6.5 (Final)
WHM 11.40.1 (build 9)
5.1.72-cll MySQL Community Server (GPLv2)
A good server configuration

What I did:
- first I thought is to much traffic and I did all kind of optimizations for apache and mysql (mysqltuner.pl , tuning-primer.sh and so on). The problem is not here. I have about 200-300 visitors instantly and the load is : average: 0.26, 0.35, 0.35 . At the midnight when all services are down and is a high load are around 80-100 visitors

- then I read about backups - so I disabled all kind of backup

- crons - disabled all crons , stop crond service , removed all crons from cron.daily

- stop all automatically check for updates and put everything on disable or manually update

- I put this values on WHM at Configure cPanel Cron Jobs : upcp 0 0 1 1 * and cpbackup 0 0 1 1 *

- disabled services like Analog,Awstats, Logaholic, Webalizer

- enabled slow queries and verify each log for mysql, messages, etc

- all databases optimized

- no I/O problems

So at the end I think is still a cron somewhere or something. Like you see on attached image mysql is going crazy . If I stop mysql before 2:00 AM with few seconds then start again after few seconds and everything is normal.

Any suggestions ?

 

After this command I removed leechprotect, Eximstats and cPBandwd. Now waiting for Santa at 2:00 AM.

Thanks a lot for reply .

 

At the end was an wordpress plugin : Wordpress Popular Posts . Thanks a lot for help.