I saw lots of different cakes called Elvis Presley Cake, some with white cake, some with chocolate cake and a few with yellow cake mix. This version is a little different than all the others in that it adds pudding mix to the batter so the cake layer is extra moist. None of the other recipes gave any sort of explanation as to why it's called "Elvis Presley Cake", so that'll have to be a mystery until someone provides a plausible explanation.
Preheat oven to 350°F. Butter or spray a 9x13-inch baking pan; set aside.
With electric mixer, mix together the cake mix, pudding mix, eggs, milk and butter until smooth, it should take about 3 minutes). Pour cake batter into prepared baking pan, and bake for 30 to 40 minutes or until knife inserted in center comes out clean.
While cake is baking, combine pineapple and sugar in a saucepan over medium heat. Bring to a boil and stir until sugar is dissolved. Let pineapple mixture cool while cake finishes baking.
When cake is baked, remove it from the oven and let cool 15 to 20 minutes. Once cake is cooled, use a fork to poke holes in several spots on the cake top. (If you poke the cake while it's still hot, the cake top will crumble and tear apart.)
Spoon pineapple mixture over cooled cake, and let stand several minutes to soak into the cake.
In a large bowl, cream together the butter and cream cheese until smooth. Add powdered sugar and vanilla, and beat until smooth.
Place dollops of the frosting in several spots over the pineapple layer. Use a spatula to gently spread the frosting in an even layer, being careful not to incorporate the pineapple into the frosting.
Sprinkle chopped pecans on top. Cut the cake into 20 or 24 slices, and serve.
NOTE: The cake will be OK if left out for up 8 hours. But after that, it needs to be covered with plastic wrap and refrigerated, and it will keep well for up to 5 days in the fridge.