ubuntu says updates available after update and upgrade

Solution 1:

Since your using ubuntu 16.04 the following should fix it:

sudo apt full-upgrade

But if you prefer the Ubuntu 14.04 way then:

sudo apt-get dist-upgrade

If the two commands don't work you should talk to digital ocean about it.

Hope that helps.

Solution 2:

It is possible your /var/lib/update-notifier/updates-available file did not refresh after your last update.

If you want to set this manually:

sudo su # Needed to acquire permissions.
/usr/lib/update-notifier/apt-check --human-readable >/var/lib/update-notifier/updates-available
exit    # to get out of sudo

Note that /var/lib/update-notifier/updates-available is set with 0600 for permissions for the user & group 'root', which prevent you from simply sudo-ing the apt-check command to rewrite it.