These are fairly old, but I've gathered they don't make a profit based on articles like the following.
http://fortune.com/2016/10/18/youtube-profits-ceo-susan-wojc...
http://fortune.com/2016/10/18/youtube-profits-ceo-susan-wojc...
It was approximated to be break even two years ago but doesn't have a growth factor as part of the number that is reported in the article, which is a key metric for determining revenue in the future. Revenue aside, profitability is extremely difficult to calculate as we don't know what the costs are as YouTube grows.
You would have made a better case here, but it's still far too old for any relevance in this discussion: https://www.wsj.com/articles/viewers-dont-add-up-to-profit-f...