Preheat the oven to 350 degrees F (175 degrees C).
Drain canned pineapple into a 1-cup measure. Add water if needed to measure 1 cup. Set aside juice and 7 pineapple rings for the cake. Set any remaining juice and rings aside for another use.
Melt butter in a 10- or 11-inch cast iron skillet over medium-high heat.
While butter is melting, combine cake mix, reserved 1 cup pineapple juice, vegetable oil, and egg whites in a mixing bowl. Beat with an electric mixer on medium speed for 2 minutes.
Remove melted butter from the heat and sprinkle brown sugar evenly over top until all butter is covered. Arrange 6 pineapple rings around the outer edge of the skillet and the remaining ring in the center without overlapping. Place a maraschino cherry into the center of each pineapple ring. Pour cake batter over the pineapples.
Bake in the preheated oven until a toothpick inserted into the cake comes out clean, 25 to 28 minutes.
Remove from the oven and let cool in the skillet for 10 minutes; don’t let the cake cool too much or it will stick to the pan.
Run an offset spatula around the edges to gently loosen cake. Place a plate over the skillet, then flip and carefully turn the warm cake out onto a plate. Transfer any fruit or glaze that sticks in the skillet back to the cake.
