I've been working with a Google Cloud debian VM and had no problem at all doing super user tasks using sudo (sudo was not asking for password).
Today I connected via SSH as usual and when I try to sudo something it started asking for password:
We trust you have received the usual lecture from the local System
Administrator. It usually boils down to these three things:
#1) Respect the privacy of others.
#2) Think before you type.
#3) With great power comes great responsibility.
[sudo] password for -----:
According to the documentation it should not ask for password as is already SSL Key authenticated connection.