Certainly orders of magnitude less than producing vinyl and selling it in brick-and-mortar stores. The size of YouTube videos is in the singles-to-tens-of-MB. http://www.cdncalc.com suggests delivery costs for commercial for-profit General-purpose CDNs are on the order of 5 cents per GB. YouTube has absolutely massive scale and their own CDN POPs deployed, so I wouldn't be surprised if their costs are a small fraction of this price. However, even at a generous 10MB per video and retail CDN bandwidth cost of 5 cents per GB, delivery of one play of one song is about would cost one twentieth of one cent. I'm sure they're making much more than this for the ad which plays before the video. YouTube also has employees and infrastructure and other costs, but they don't disclose their financials, so it's hard to know exactly how much they spend on hosting: http://www.businessinsider.com/google-cfo-doesnt-disclose-yo...
All that said, digital distribution tends to be drastically cheaper than physical distribution to the point where it's essential free, and a negative cost once ad revenue is factored in.
For a vinyl analogy, imagine Starbucks was paying 1000x the cost of distributing a record if someone went to Starbucks after seeing the ad which was slipped inside the record cover.
Another consideration: YouTube makes so much on ads that they're giving some of that money back to content producers because they know that the service they provide is so readily available for free elsewhere that producers need additional incentives to use YouTube specifically.
I'm fairly confident that their ad share payouts exceed their bandwidth costs.
