I don't think your cousin is being cocky. I think your cousin do not or is unable to find a healthy outlet to release his emotions.
His way of dealing with the break up is via excessive drinking and partying as well as ridculing you.
People deal with pain differently, sometimes in a postive way and some in a self-destructive mode.
Maybe you should have a heart to heart conversation with him. If you are uncomfortable ask a close female friend or relative.