Preheat the oven to 350°F and place the rack in the middle position. Prepare 2 8 inch cake rounds by spraying with nonstick baking spray, laying in parchment, and spraying again.
In a large bowl, stir together cake mix, vanilla pudding mix, and ground strawberries.
Whisk in pureed strawberries, eggs, oil, water, and vanilla until smooth.
Divide evenly into prepared pans, place in the oven, and bake for 30 minutes. Insert a toothpick into the center to see if it comes out clean (tiny moist pieces of cake are ok too). If not, let the cakes bake another 3 minutes until done. Remove from the oven and let cool for 10 minutes in the pan. Then, remove from the pan and cool completely on a wire rack, about 30 minutes.
In the bowl of your stand mixer fitted with the whisk attachment, add cream cheese and butter and beat on medium low speed until fluffy, 3 minutes. Turn off the mixer and add half of the powdered sugar and ground strawberries. Turn to low speed until the sugar and strawberries are incorporated, about 1 minute.
Add in remaining powdered sugar, vanilla, and salt and mix on low speed until incorporated. Turn to medium speed and beat until light and fluffy, 4-5 minutes.
Once the cakes are fully cooled, using a serrated knife, cut each cake in half horizontally so you have 4 rounds.
Place the first round on your cake plate and top with icing. Spread into an even layer about ½-inch thick. Repeat with the remaining cake layers and icing. Top the last cake round with most of the rest of the icing and smooth over the top and let some hang over the edge. Using an offset spatula, spread the icing all around the sides of the cake vertically, using the remaining icing to fill as you go. Once smooth, decorate with sliced strawberries, slice, and serve.