Preheat the oven to 350°F (175°C) and prepare baking pans.
In a bowl, whisk together flour, baking powder, baking soda, salt, and cocoa powder.
In a large bowl, beat the softened butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition, followed by vanilla extract.
Gradually add the dry ingredients to the wet mixture alternately with the milk.
Divide the batter equally among three bowls; mix in strawberry puree, leave one bowl plain, add cocoa to another.
Pour batter into prepared pans and bake for 25-30 minutes.
Cool the cakes in pans for 10 minutes, then transfer to wire racks to cool completely.
Level the tops of the cakes if necessary before frosting.
Spread chocolate frosting on the chocolate layer, followed by vanilla, and finally strawberry.
Once layered and frosted, chill the cake for about 30 minutes before serving.
