Run an Ubuntu container, you're basically pulling the ubuntu container from online and say you make a change to it (like installing software into it). Now, just like in GitHub, before you push your changes, you've to 'commit' them.
Just committing the changes you've made to the container shall make a container that is ready to be pushed. And, no additional building is required.
To commit, use:
sudo docker commit <container-id> username/container-name-that-you-want
To push, use:
sudo docker push username/same-container-name-that-you've-specified-above.
For more information, check out this Docker Tutorial.