Preheat oven to 350°F Butter and flour a 12-cup Bundt pan; set aside.
Place brownie mix, pudding mix, beaten eggs, melted butter, and sour cream in a large bowl; stir with a wooden spoon until smooth, then pour into (greased and floured) prepared pan.
Bake for 45 minutes or until a toothpick or cake tester comes out with a few moist crumbs attached. Cool the pan on a wire rack for 30 minutes; then unmold the cake, invert it, and cool completely on a wire rack. Serve immediately, or cover in plastic wrap and store at room temperature. The cake will stay fresh for up to 4 days. It can also be tightly wrapped in wax paper, sealed in plastic wrap, and frozen for up to 2 months; allow the cake to thaw at room temperature before serving.