Preheat your oven to 375°F (190°C) and grease a 9x9-inch baking pan.
In a mixing bowl, combine the cornmeal, all-purpose flour, sugar, baking powder, baking soda, and salt.
In another bowl, whisk together the sour cream, melted butter, and eggs until well combined.
Gradually add the wet mixture to the dry ingredients, stirring until just combined. Be careful not to overmix; a few lumps are okay.
Gently fold in the corn kernels and shredded cheddar cheese (if desired).
Pour the batter into the greased baking pan, spreading it evenly.
Bake for 25-30 minutes or until the top is golden brown, and a toothpick inserted into the center comes out clean.
Allow the cornbread to cool for a few minutes before slicing it into squares.