1. Preheat oven to 350°F (175°C). Grease and flour three 8-inch round cake pans.
2. In a large bowl, sift together the flour, baking powder, and salt.
3. In another bowl, beat the sugar and butter until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
4. Gradually add the dry ingredients to the wet ingredients, alternating with milk. Mix until just combined. Fold in the strawberry puree.
5. Divide the batter evenly among the prepared cake pans.
6. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow cakes to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.

For the Strawberry Filling:

1. In a saucepan, combine the sliced strawberries, sugar, cornstarch, and water. Cook over medium heat, stirring constantly until the mixture thickens and comes to a boil. Remove from heat and let cool.

For the Whipped Cream Frosting:

1. In a mixing bowl, beat the heavy cream, powdered sugar, and vanilla extract until stiff peaks form.

Assembly:

1. Place one cake layer on a serving plate. Spread half of the strawberry filling over the top.
2. Add a layer of whipped cream frosting over the strawberry filling.
3. Place the second cake layer on top and repeat with the remaining strawberry filling and whipped cream frosting.
4. Place the third cake layer on top and frost the top and sides of the cake with the remaining whipped cream.
5. Garnish with fresh strawberries and drizzle with strawberry sauce if desired.