Heat oven to 350°F (325°F for dark or nonstick pan). Grease and lightly flour bottom and side of 10-inch angel food (tube) cake pan or 12-cup fluted tube cake pan, or spray with baking spray with flour (do not use cooking spray).
In large bowl, beat cake mix, dry pudding mix, water, butter, eggs and 2 to 3 teaspoons rum extract with electric mixer on low speed 30 seconds, then on medium speed 2 minutes. Spread in pan.
Bake 43 to 53 minutes or until toothpick inserted in center comes out clean. Cool in pan 30 minutes. Run knife around side of pan to loosen. Turn pan upside down onto cooling rack; remove pan. Cool completely, about 1 hour.
In small microwavable bowl, microwave frosting uncovered on Medium (50%) 15 seconds. Stir in 1/2 teaspoon rum extract. Spread over top of cake, allowing some to drizzle down side. Sprinkle with pecans. Store loosely covered.