Heat a 9-inch iron skillet in the oven for 10 minutes. Melt butter in skillet and brush over sides of skillet. Pour excess butter into a large bowl. Whisk buttermilk and eggs into excess butter.
Mix sugar, baking soda, cornmeal, whole-wheat flour, and salt in another bowl. Whisk cornmeal mixture and frozen corn into buttermilk mixture. Scrape cornbread mixture into skillet.
Bake in preheated oven until a toothpick inserted into the center of skillet comes out clean, 20 to 25 minutes.