Position a rack in the center of the oven and preheat to 400 degrees F. Butter a 9 by 9 by 2-inch metal baking pan.
Blend the cornmeal, flour, sugar, baking powder, salt and baking soda in a processor for 5 seconds. Add the butter cubes. Blend until the butter is reduced to tiny pieces, 15 to 20 seconds. Whisk the buttermilk, sour cream and eggs in a large bowl to blend. Add the dry ingredients from the processor and stir until evenly moistened. Scrape the batter into the prepared pan.
Bake the corn bread until the top is golden brown and a tester inserted into the center comes out clean, about 25 minutes. Cool the bread on a rack at least 30 minutes. Serve warm or at room temperature.