My Ubuntu droplet is sending emails for things like cron output to email address my-user-name@ubuntu. The emails pile up in file /var/mail/my-user-name. How can I change this so the emails go to my external email address instead?
You can forward root's mail inbox to your email address. To do this, you can open the /etc/aliases file with your editor. You will find this inside the file.
# See man 5 aliases for format
postmaster: root
Add the following line to the file. This will forward all emails generated from your system that is sent to root to your specified email address.
# See man 5 aliases for format
postmaster: root
root: user@youremaildomain.com
Afterward, save and close the file. Finally, run the newaliases command in your terminal to activate the change.
Hope this could be useful. Do not forget to check your Spam folder if you do not receive the expected emails in your inbox.