Yield: 6-inch cake
Preheat oven to 350 degrees F. Butter three 6-inch cake pans and line with parchment paper. Set aside.
Puree half of mixed berry mixture. Set aside.
In a large bowl, whisk together flour, baking soda, baking powder, and salt. In the bowl of a stand mixer fitted with paddle attachment (or using an electric hand mixer), beat butter until smooth. Add sugar and lemon zest and beat until light and fluffy. Scrape down bowl as needed to ensure thorough mixing.
With the mixer running on low speed, add eggs one at a time. Add sour cream, mixed berry puree, and lemon juice. Mix until incorporated. Add flour mixture and mix on low speed until combined. Fold in remaining mixed berries.
Evenly distribute batter among prepared cake pans. Level batter and bake for 40-45 minutes until cakes are golden brown and toothpick inserted in center of cake comes out clean. Let cool in pan for 8 minutes before unmolding. Run offset spatula or butter knife along the perimeter of cake to help loosen. Allow cakes to cool to room temperature on wire rack.
In the bowl of a stand mixer fitted with a paddle attachment (or using an electric hand mixer), beat together cream cheese and butter until smooth. Scrape down bowl as needed. Add powdered sugar, salt, and vanilla. Mix on low speed until frosting is smooth.
Fit a decorating bag (piping bag) with a small round tip. Fill the bag with about 1/2 cup of frosting. Set aside.
If necessary, level the tops of cooled cakes. Place one cake layer on a cake stand or cake plate. Spread a thin layer of cream cheese frosting over cake using a small offset spatula. Using the filled piping bag, pipe two concentric circles along the perimeter of the cake round. This will serve as a barrier.
Spread two tablespoons of raspberry jam to fill the frosting boundaries. Place second cake layer on top. Repeat filling cake layer with frosting and jam. Place the final third cake layer on top. This layer will not have jam.
Spread frosting around the cake to create a "crumb coat" layer to seal in any crumbs. Chill cake in the fridge for 15-20 minuets to set frosting. If desired, add additional frosting to coat cake. Keep cake chilled until ready to serve.
Decorate top of the cake with fresh berries. Let chilled cake sit at room temperature for at least 20 minutes before serving to allow cake and frosting to soften.