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.