Not having 3 pans is no problem. If you have for example have two pans then add 1/3 of the batter to each of the two pans and let the last 1/3 batter stay in your mixing bowl. Then when the two cakes have baked and cooled down for 5 minutes, release them from the pan and let them cool down on a wire rack. Then you can wash one of the baking pans, add new baking paper, and pour the remaining batter in the pan and bake the last layer. It completely okay for the batter to sit on your kitchen counter while the other cakes bake.