The only thing of significant value that they give away is $20 credits to new riders and some new driver bonuses.
The number of full-fare (no subsidy to either rider or driver) Uber trips surely absorbs these incentives, leaving a positive gross margin. (There's also a miniscule computing, bandwidth, and payment processing cost to a marginal ride, marginal being defined as the nominal X+1th ride after all the costs for X rides are already paid for.)
Perhaps absolute certainty is a slight overstatement, but here's one where I'd bet eating my hat on it. I edited to insert an "almost".
Here in China Uber has various subsidy programmes for drivers and customers. These eat into margins and make them negative for some (but probably not all) trips.
Example: a few weeks ago, I paid ~3USD for a 13km ride that took 90 minutes (due to Beijing traffic). The driver was definitely paid more than that for the ride.
