My carburetor keeps dumping gas

That is an old-style non-racing Holley, and they are adjusted internally, like the majority of street carbs.
What's under that epoxy, is the same as what you see on the rear bowl. I wouldn't say that those plugs are prone to leakage, but ..... I've seen a few epoxied up like that.
I changed the carburetor and it runs great! Thanks everyone for all the information.