Hi Tracy,
In American English, "cute" means "pretty" or "attractive" or even "beautiful". But it sometimes implies the idea of "smallness" so anything small can also be described as "cute" too, if it is also pretty. For example, you could talk about a "cute house" if the house is pretty and relatively small compared to other houses... but you probably wouldn't ever say that a castle is "cute," even if the castle were very beautiful.
Women may often complement each other using "cute": "That's a cute jacket, you look cute today, that is a cute haircut." And men sometimes refer to women as cute, too.
Since "cute" means attractive and pretty, you can use it to describe an adult man... but you may need to be a little careful. Since it carries the idea of "smallness" some men might not like being described "cute" very much. By the way "pretty" also sounds like a very feminine description that many males might not like very much.
A similar word for "attractive" that is used almost always for men and very rarely for women is "handsome." "Attractive" is a good word that is gender neutral. You can use attractive for men or women basically equally.