You didn't say what version of Ubuntu you are running but since you are managing servers that are ostensibly in a production environment, I'll assume it's 16.04 LTS or something similarly stable. If so, the Software updater should take care of making sure that everything is patched to the latest stable version.
You can of course (as root) cron
apt-get update
and
apt-get upgrade
https://help.ubuntu.com/community/CronHowto
but there is a small downside using that approach as discussed on other threads on this site. Primarily, the issue is that packages available through the software updater have gone through an additional step of limited user testing that you don't get by using apt-get.
And of course some updates, notably kernel updates, that require a reboot to take effect. In a production environment you'll probably want to schedule any reboot for a maintenance window.
There is also a risk that an unattended upgrade could go wrong so I've always found value in watching the messages as package upgrades are performed to ensure that everything went smoothly.
ssh
into a server and run updates manually? – Robert Dewitt Jun 22 '17 at 00:18