Extract and paste have entirely different physical characteristics so you would have to come up with a totally different recipe. ALmond paste is ground almonds, so the cake would become dense and heavy, a consistency like clay. it would even be hard to incorporate it into the dough or batter.
Almond extract is something you use by the teaspoon and is a liquid. If you like the taste of almond extract, you would need a lot of almond paste to get it, and only if the almond paste has included bitter almonds, which not all has.