If one eats to satiation food with no bread, can he say Birkat HaMazon

Shalom, Thank you for your question. Birkat HaMazon is only said after a meal of bread. The obligation to recite Birkat HaMazon applies from the Torah when a person is satiated, however the Rabbis added an obligation to say it even after eating only a keziyit (about 28 cubit cm) of bread. There is one situation when Birkat HaMazon should be recited even if one did not eat bread. That is, when a person eats a large quantity of “mezonot”, that is food from “bread family” that is not bread because it is cake like, or cracker like, then one also says Birkat HaMazon. (It must also be from the 5 grains). This is called Pat HaBa BeKisnin. So, if a person had a full meal of cake, then they would need to say Birkat HaMazon. The laws of this rule are rather detailed, but that is the general idea. In summary - Birkat HaMazon is recited after eating bread, and in some special situations after eating a large amount of cake or cracker like food. I hope this is of some help.