Bubble' The term 'bathday cake' is a type of cake that is made with SOAP, usually in the shape of a cake. It is often used as a fun way to celebrate a birthday or other special occasion. The crossword solution for the term 'bathday cake' is 'SOAP, ' which is a substance that is composed of a mixture of fats and oils that create a lather when mixed with water. The bubbles created by the SOAP are what give the cake its name.