No, you have to learn them - sorry. But there are not soo many of them. Dative: aus (from location), bei (at location or persom, i.e. 'bei ihm'), mit (with), nach (after - time, to - location, but usually used without article 'nach Hause'), von (from), zu (to) Accusative: bis (till, until), durch (through), für (for), gegen (against), ohne (without), um (at - time) both dative and accusative: an, auf, hinter, in, neben, über, unter, vor, zwischen ---> But don't ask me how to recognize when you use dative or accusative. Hope, I could help you more.

Liawell, you forgot one: Dative: Seit. We had to learn these lines by heart at school: Aus, bei, mit, nach, seit, von, zu. Bis, durch, für, gegen, ohne, um. You just need to find a certain rhythm and then it's quite easy to remember.