Ubuntu 16.04 mysql 5.6 - my.cnf changes are not taking effect

You need to check the error in syslog : /var/log/syslog

If you get something like this

kernel: [83454.649662] audit: type=1400 audit(1583063492.688:61): apparmor="DENIED" operation="open" profile="/usr/sbin/mysqld" name="/etc/mysql/my.cnf.fallback" pid=27270 comm="mysqld" requested_mask="r" denied_mask="r" fsuid=1000 ouid=0

Here is the solution for you.

Solution :
The root cause is a bug in the MySQL 5.6 for Ubuntu 16.04

The issue is with apparmor. It is denying access to a symlinked file.
Run following command as root.

echo '/etc/mysql/** lr,' >> /etc/apparmor.d/local/usr.sbin.mysqld

or try following with sudo user

sudo echo '/etc/mysql/** lr,' >> /etc/apparmor.d/local/usr.sbin.mysqld

But if it still does not work

sudo nano  /etc/apparmor.d/local/usr.sbin.mysqld

and add following line at the end of the file.
Now reload apparmor

sudo systemctl reload apparmor

Make some changes in my.cnf and restart mysql. Changes should take effect.