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Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan or line with parchment paper.
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In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
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In a large bowl, cream the butter and granulated sugar together until light and fluffy.
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Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
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Gradually add the dry ingredients to the wet ingredients, alternating with the sour cream and mixing until just combined.
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Gently fold in the diced strawberries, blueberries, raspberries, and blackberries, being careful not to crush the berries.
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Stir in the lemon zest and lemon juice.
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Pour the batter into the prepared cake pan, spreading it evenly.
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Bake for 1 hour and 15 minutes, or until a toothpick inserted into the center comes out clean.
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Remove the cake from the oven and let it cool in the pan for 10 minutes. Then, transfer it to a wire rack to cool completely.
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Once cooled, dust the top of the cake with powdered sugar before serving.
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Slice and serve the cake with whipped cream, if desired.