Syncing over the home network wouldn't be enough; one of the big features of Dropbox is that you can sync devices anywhere. Eg: my phone, my office PC, and my home PC all share the same Dropbox folder.

Since we're not all IPv6 yet, the cube will need to set up a secure tunnel out of the home network to a public endpoint, probably on a server run by your company. All syncing would have to go through that server, preferably with end-to-end encryption so the server can't access the data. (It can still be captured for offline cracking, though.)