If a guy is cocky or confident, can he get shy around a girl he likes?

My crush is the typical I know I am good looking so I'll act cocky. But he gets shy with me. He can talk to anyone but with me he can't seem to remember how to speak. He tries to play it off like he's cool and chill. Can a cocky and confident person be shy around their crush. He acts different around me and his friends have noticed that there is something going on between us. Why would he talk to other girls and not me?
If a guy is cocky or confident, can he get shy around a girl he likes?
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