Strawberry Limeade Cake with Strawberry Cream Cheese Frosting

Preheat oven to 350 degrees F. Lightly grease three 8-inch round cake pans and line bottoms with parchment paper rounds. Whisk together flour, baking soda, baking powder, and salt in a bowl. Process strawberries in a food processor until small pieces and a thick puree form, 5 to 10 seconds. Whisk together buttermilk and 1 cup strawberry puree in a bowl. Reserve remaining puree for Strawberry-Cream Cheese Frosting. Beat butter and sugars with an electric mixer on medium speed until light and fluffy, 1 to 2 minutes. Add eggs, one at a time, beating to incorporate after each addition. Beat in vanilla and lime zest. Reduce speed to low and beat in flour mixture and buttermilk mixture alternately, starting and ending with flour mixture, just until flour is incorporated. Divide batter among prepared pans. Bake until a toothpick inserted in the center comes out clean, 20 to 23 minutes. Cool in pans on a wire rack for 15 minutes, then invert onto rack to cool completely. Place one layer on a cake plate and frost top with 1 cup frosting. Repeat two more times. Cut a 12-by-24-inch piece of plastic wrap and fold in half to make a 6-by-24-inch strip. Wrap around cake to secure layers. Chill until frosting is set, 4 hours or up to 1 day. Top with whole strawberries just before serving.