Preheat the oven to 325 degrees F (165 degrees C). Grease and flour three 8-inch pans.

To make the cake: Combine cake mix, milk, oil, eggs, and instant vanilla pudding mix in a large bowl; beat with an electric mixer on low speed until blended. Scrape down the sides of the bowl; continue to beat for 4 minutes on medium speed. Pour batter into prepared pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 20 to 25 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen; invert cakes carefully onto a cooling rack and let cool for about 30 minutes.

To make the frosting: Beat cream cheese, confectioners' sugar, and white sugar in a large bowl until smooth. Fold in whipped topping, pecans, and chopped chocolate. Spread frosting onto the cooled cake layers. Stack layers; frost top and sides.