Preheat the oven to 350 degrees F (175 degrees C).

Combine cake mix, eggs, 1 package pudding mix, vegetable oil, orange extract, and mandarin oranges, and beat well for about 3 minutes.

Bake in three 9-inch greased and floured round cake pans for 20 to 25 minutes in the preheated oven.

Fold remaining package pudding mix and pineapple into whipped topping for frosting.

Frost chilled cake and keep refrigerated until ready to serve.