Preheat the oven to 350°F (175°C). Lightly grease and flour either two 9-inch round cake pans or one 9x13-inch rectangular pan to prevent sticking.
In a large mixing bowl, combine the yellow cake mix, eggs, oil, and the full contents of the mandarin orange can (including the juice). Beat with a mixer on medium speed for approximately 2 minutes, or until the mixture is airy and smooth.
Pour the batter evenly into the prepared baking pans. Place in the oven and bake for 25 to 30 minutes, or until a toothpick inserted into the center emerges clean. Allow the cake(s) to cool fully on a wire rack.
While the cake cools, prepare the frosting by blending the dry pudding mix with the well-drained crushed pineapple in a medium bowl. Stir until thoroughly incorporated. Gently fold in the whipped topping until smooth. Refrigerate the frosting for no less than 30 minutes to allow it to firm up.
To assemble, if using round layers, place one cooled cake round on a serving dish and spread a portion of the chilled frosting on top. Add the second layer and apply the remaining frosting across the top and sides. For a sheet cake, simply spread the frosting evenly over the surface of the cooled cake.
Place the finished cake in the refrigerator for a minimum of 2 hours—or preferably overnight—before serving. This chilling time enhances the flavor and helps the topping set to the perfect consistency.