Preheat your oven to 400°F (200°C).
In a skillet, brown the ground beef over medium heat until fully cooked.
Add the drained black beans, kidney beans, corn, and salsa to the skillet.
Season the mixture with cumin, chili powder, salt, and pepper.
Stir well and cook for another 5 minutes.
Transfer the beef and bean mixture to a greased 9x13-inch baking dish.
In a mixing bowl, combine the cornbread mix, egg, and milk until just blended.
Spread the cornbread batter evenly over the beef mixture.
Sprinkle the shredded cheese on top of the cornbread layer.
Bake in the preheated oven for 30-35 minutes or until golden brown.