A birthday cake in French is 'un gâteau d'anniversaire'
you have a birthday cake
"la grand-mère sert le gâteau d'anniversaire"
Gateau is food cake in french
Canadians (for the most part speak English) so a birthday cake would be called a birthday cake. However, for the francophones (french speakers) in Canada a birthday cake would be called: gâteau d'anniversaire
gâteau
A banana cake is "un gâteau à la banane" in French.
a birthday is 'un anniversaire' in French
Birthday is "anniversaire" (masc.) in French.
gâteau sucré
If you mean a slice of cake it is - tranche
gâteau basque.
acheter un gâteau