If it is a mobi file, only the Kindle reader can handle files with DRM. If there is no copy protection in place, there are scads of readers that you can use - but Google Books isn't one of them.
All google books are stored "in the cloud" not on the device, Books will not read local files.
If you have ADE DRMed epub files, Aldiko has ADE. I just loaded 50+ Sony Reader epub files onto my Tab for my wife. Aldiko imports them with no problems