Preheat oven to 350 degrees F (175 degrees C), or 325 degrees F (165 degrees C) for coated pans. Spray two 8-inch round cake pans with cooking spray.
Stir sugar, frozen coconut, and sour cream for filling together in a medium bowl until well combined. Set aside in the fridge until ready to use.
Combine cake mix, pudding mix, water, oil, eggs, egg whites, and vanilla for cake in the bowl of a stand mixer fitted with a whisk attachment. Blend on medium speed for 3 minutes, scraping down the sides of the bowl as necessary. Pour batter into the prepared pans.
Bake in the preheated oven until golden brown and a toothpick inserted into the center comes out clean, about 25 minutes. Remove from the oven and cool in the pans for 5 minutes, then invert onto a parchment-lined cooling rack to cool completely, about 30 minutes.
Use a large, serrated knife to cut each cake layer in half lengthwise; you will have 4 pieces. Flip top pieces so all cut sides are facing up. Stack layers and filling on a serving platter as follows: 1 bottom layer, 1/3 of the filling, 1 top layer, 1/3 of the filling, remaining bottom layer, remaining filling, remaining top layer. Cover and chill, 30 minutes to overnight.
Combine sugar, corn syrup, egg whites, water, vanilla, and cream of tartar for frosting in a large heat-proof bowl; stir until well combined. Place the bowl over a double boiler and whisk using an electric hand mixer until thick and glossy, about 7 minutes. Take care that the double boiler doesn’t reach higher than a slow simmer.
Spread frosting over cooled cake immediately and sprinkle with shredded coconut.