Can a 15 year old date a 21 year old?

In Massachusetts, it would depend on what was happening on those dates.  If the parties engaged in any sexual conduct, the 21 year old could be charged with statutory rape.  If the parties were simply dating, as long as the parents of the 15 year old were agreeable, there is nothing to prevent this,  Because the 15 year old is a minor, they would have say as to what is permissable dating for the minor.