Preheat the oven to 425°. Butter an 8-by-2-inch square cake pan. In a food processor, add the butter, egg, blue cornmeal, all-purpose and whole wheat flours, baking powder, salt and baking soda; pulse to combine. Add the buttermilk and process for 5 seconds, or just until smooth.
Scrape the batter into the pan and bake for 25 minutes, or until the center is firm. Transfer the bread to a rack to cool a bit, then turn out and let cool completely.
The bread can be made up to 1 day ahead. Wrap in plastic and keep at room temperature.
Blue cornmeal is available at specialty food markets.