It depends. Cakes made with a puree and topped with a buttercream frosting can be stored covered on the counter for three days. If the cake has pieces of strawberries in it or has been frosted with a cream cheese frosting, then you should keep the cake in the refrigerator. If you put strawberries on top of the cake for decoration they will more than likely get moldy at room temperature, so store the cake in the fridge.