Preheat oven to 325°F. Coat a 9-inch by 13-inch cake pan with nonstick spray.
In a large bowl, whisk the eggs and oil together until well blended. Whisk in the cake mix until smooth. Carefully fold in the mandarin oranges and their juice.
Pour the batter into the prepared pan and bake 25 to 35 minutes (check at 25 minutes). Cool completely, at least 30 minutes.
When the cake is cool, blend whipped topping and dry vanilla pudding mix in a large bowl (do not prepare the pudding mix into pudding). Carefully fold in pineapple and juice. Spread the frosting in a thick, even layer on the cake.
Cover and refrigerate at least 30 minutes before serving. Garnish individual slices with maraschino cherries if desired. Refrigerate any leftovers.