Quarter the strawberries, put them in a pan with sugar and squeeze the juice from an orange over them. Let everything boil together until it takes on a syrupy consistency. Then purée the strawberries and pour them through a sieve.
Put the butter, flour, eggs, sugar, vanilla extract, baking powder, and cream cheese in a bowl and mix everything into a batter with an electric whisk. Divide the mixture equally between three bowls. Stir the cocoa into one of them, and half the strawberry purée into another.
Put each portion of batter into a greased springform pan with a diameter of 8 inches. Then bake all three for 40 minutes at 350°F. Let all of the cakes cool before removing them from the pans.
Beat the butter with the vanilla extract and the powdered sugar until it's fluffy, then stir in the cream cheese when the mixture turns white. Divide the cream between three bowls into equal portions. Stir the rest of the strawberry purée into one, and more cocoa powder into another.
Place the chocolate cake layer on a cake plate and cover the top and all around the edge with two-thirds of the chocolate buttercream. Place the strawberry cake layer on top and cover it with two-thirds of the pink strawberry buttercream. For the uppermost layer, place the third cake on top of the other two. Cover it on top and around the edge with the white buttercream, but only use about half of it for this.
Put the rest of the chocolate buttercream in a piping bag with a serrated nozzle and create roses close together around the chocolate cake base. Do the same with a second piping bag and the strawberry buttercream. Then put the rest of the white buttercream in a third piping bag and cover the edge of the upper layer as well as the top with white cream roses.
