to check if cron is actually running anything at this moment in time (works on ubuntu)
pstree -apl `pidof cron`
and you’ll either get
2775,cron # your pid (2775) will be different to mine :-)
or a tree output with all the child processes that cron is running (it may not name them if you don’t have sufficient privileges)
and as Hamoriz says the logs are in /var/log/syslog so
grep CRON /var/log/syslog
will get you the logs just for cron