Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Whisk sugar, flour, cornmeal, baking powder, cornstarch, cinnamon, and nutmeg together in a bowl. Add coconut milk and evaporated milk; fill empty cans with water (totaling 26 fluid ounces) and add to mixture. Mix butter, egg, and vanilla extract into mixture and beat with an electric mixer until well mixed; pour into the prepared dish.
Bake in the preheated oven until cornbread is cooked through and set, 1 hour 30 minutes.
