I think of a way:
There are some online file conversion utilities, (you can find through Google..) that help to convert a file to tar.bz2
or zip
etc.. formats.
If that online utility has integration with Google Drive / Dropbox, you should be able to convert the compressed file to cloud.
Another way is to use a cloud service. Some free services give you up to 256 MB RAM, enough to run a customized compression utility in a container, and then send it to Google Drive using their APIs. In this method you will have control over the process, however it takes some time to deploy the utility.