I believe that both DropBox and Google Drive actually break up large files and upload them in chunks. Thats how DropBox is able to do things like "streaming sync". It all happens without the knowledge of the end user.
I would also look into resumable uploads from the Google Documentation: https://developers.google.com/drive/web/manage-uploads#resumable
Streaming Sync Announcement: https://blog.dropbox.com/2014/07/introducing-streaming-sync-supercharged-sync-for-large-files/