Safe mode will probably still load all Google apps because they're pre-installed. If the problem is a google app, then it might be a good idea to force stop and turn off all google apps, (except google play services), clear the play services cache/data, and then see if it continues to increase data storage. If data storage doesn't increase with all of them off, turn each one back on, one at a time, and monitor play services reaction. Note that not all google apps have the word "google" in them. Apps like Drive, Hangouts, and Maps should also be turned off during troubleshooting.
As B. Diddy mentions, Safe mode troubleshooting is a good idea if its due to a 3rd party app.