Center a rack in the oven and preheat the oven to 400°F. Spray an 8x8-inch baking pan with nonstick cooking spray and set aside.
In a large bowl, whisk together the flour, cornmeal, sugar, baking powder, baking soda, and salt. Set aside.
In a medium bowl, whisk together the buttermilk, melted butter, oil, and eggs. Pour the liquid ingredients over the dry ingredients and stir until combined. The batter will be lumpy. Stir in the corn kernels. Pour batter into prepared pan.
Bake cornbread for 25 to 30 minutes, or until the top is golden brown and a toothpick comes out clean after inserted into the center. Let cornbread cool in pan for 15 minutes before cutting. Cut into squares and serve.