How to see full cron log (Not of just 1 day or less)?

Another alternative is

sudo zgrep CRON /var/log/syslog*

zgrep uncompresses files if needed. Options same as for grep.

You can do this to newer syslog files:

cd /var/log
cat syslog.1 syslog | grep CRON

To the oldest you must do it:

cd /var/log
zcat syslog syslog.4.gz syslog.3.gz syslog.2.gz | grep CRON

It's a good idea to do these commands nested in loops, specially to zcat, since syslog.#.gz are more numerous.

You can even store them into another file to analyze better:

cd /var/log
zcat syslog syslog.4.gz syslog.3.gz syslog.2.gz | grep CRON > ~/cronanalysis.txt
cat syslog.1 syslog | grep CRON >> ~/cronanalysis.txt

The order of syslog files is inverted, so you put older to head and newer events to tail.