I found this interesting link about black birch on Wikipedia: Betula lenta
Back in summer camp, we used to strip the sweet, inner bark of the twigs with our teeth and savor the root beerish flavor. In the absence of candy, even adolescent girls can get creative. Along with wintergreen and sorrel, it was one of the flavors of summer... more memorable than the Pepsi and Doritos that took their place in later years.
A Connecticut Indian told me many years ago that his family used to make syrup from the black birch tree sap, like maple syrup. This article is the only other reference to that I have ever heard of.