Also the second sentence could be in conditional: We would eat all the cakes they would send us. Nos comeríamos todos los pasteles que nos enviaran. (if they would send us cakes, then we would eat them all)

The first sentence is correct, the tenses don't match: 1) Nos comimos todos los pasteles que nos habían enviado. - Eng: We ate all cakes they had sent us. - Comimos (past) - Habían enviado (past) 2) Nos comimos todos los pasteles que nos enviarán. - Eng: We ate all cakes they will send us. - Comimos (past) - Enviarán (future)

The first is correct: Nos comimos todos los pasteles que nos habían enviado; if you want to say something you did (Nos comimos todos los pasteles) you have to use the verb in the past form (que nos habían enviado), because in the second sentence: (que nos enviaran) is something that is going to happen in the future.