Preheat the oven to 325℉. Spray a 10-inch tube pan (angel food cake pan) with baking spray (nonstick spray with flour).
In a large bowl, whisk together flour, sugar, salt and baking soda.
Add the eggs, butter, sour cream, lemon zest and vanilla to the flour mixture. Use an electric mixer on medium-speed to beat for 1 minute, until blended. Scrape the sides and bottom of the bowl with a spatula. Beat on high speed for 2 minutes. Gently stir in half each of the raspberries and blueberries.
Spread the batter evenly in the prepared pan. Sprinkle the remaining berries evenly over the batter.
Bake for about 1½ hours if you have a dark gray pan (1 hour, 40 min if you have a light colored pan). A piece of uncooked spaghetti inserted into the center should come out clean. Let the cake cool in the pan on a wire rack for 15 minutes, then invert the cake onto a rack to cool completely. Just before serving, dust the cake with powdered sugar.