As Micahel helpfully explains, "the cake would have burnt" is referring to the action of the cake burning, whereas "the cake would have been burnt" refers to the final result - a burnt cake! --- Want to learn English the SMART (Stretch, Measurable, Achievable, Realistic, Timely) way with me? Go to my teacher profile and book your $1 trial lesson now! http://bit.ly/paulblakemanitalkiteacher

to be burnt - burnt is a past participle which is being used as an adjective to describe the state of the cake. to burn - verb to describe the activity in this case within itself (the cake); there is no direct object There is no significant difference in meaning in this case.