Preheat oven to 425 degrees F (220 degrees C).

Place a 10-inch cast iron skillet in the oven to preheat.

In a large bowl, combine the cornmeal, flour, sugar, baking powder, baking soda, and salt. Whisk until well combined.

In a separate bowl, whisk together the buttermilk, milk, and eggs.

Add the wet ingredients to the dry ingredients and mix until just combined.

Melt 6 tablespoons of the butter in the microwave or in a small saucepan over low heat. Add to the batter and mix well.

Reduce the oven temperature to 375 degrees F (190 degrees C).

Carefully remove the hot skillet from the oven. Add 2 tablespoons of butter to the bottom of the skillet.

Pour the batter into the skillet and spread evenly.

Bake for 20 minutes, or until a toothpick inserted into the center comes out clean.

Let the cornbread cool in the skillet for a few minutes before slicing and serving.