Preheat your oven to 350°F (175°C) to ensure the cake bakes evenly.
Grease and flour a 9×13-inch baking dish. In a large bowl, mix the white cake mix, flour, and strawberry Jello powder. Add water, oil, eggs, vanilla extract, and strawberry puree. Mix until smooth.
Pour the batter into the baking dish. Bake for 35 to 40 minutes, until a toothpick inserted in the center comes out clean or with a few crumbs. Cool completely for at least 60 minutes before frosting.
Beat the cream cheese and butter until smooth. Mix in 1/4 cup strawberry puree, then gradually add powdered sugar until the frosting reaches a spreadable consistency. Chill briefly if needed.
Spread the chilled strawberry cream cheese frosting evenly over the cooled cake.
Slice the cake and serve with optional garnishes, such as fresh strawberries, a sprinkle of Jello powder, or white chocolate shavings.
Notes
Cool the cake completely before frosting. Refrigerate the cream-cheese-frosted cake within 2 hours and use it within 3 to 4 days.