Un papa gâteau can literally be translated by “cake daddy”. This expression is used to refer to a doting father! It appeared in the 19th century. It is based on the verb gâter that means “to spoil”. “To spoil” can have negative connotations in English, but in French, it depends on the context. It can mean either spoiling to excess or pampering a child, but within reason!
French with Valerie 