I would like to know if I can paint over old hard black glue from a concrete floor, I would be using concrete paint. Thanks!

What's the condition of the black glue? Is any of it peeling or crumbling? Do you know if it's tile adhesive, or waterproofing? Have you done a moisture test of a bare concrete patch? Tape a foot square of plastic with duct tape to the floor for 24 hours to see if moisture collects under it. If it does, probably no paint is going to last long.