Prepare the white cake mix according to the package directions. Pour the batter into a greased 9×13-inch baking pan and bake according to the package instructions, usually about 28–32 minutes, until a toothpick inserted in the center comes out clean.
Remove the cake from the oven and let it cool in the pan for about 20–30 minutes. It should be cool enough to handle but remain in the baking pan for the remaining steps.
Using the handle of a wooden spoon or a thick skewer, poke holes evenly across the entire cake, spacing them about 1 inch apart. Make the holes deep enough for the raspberry gelatin to soak into the cake without going completely through the bottom.
Dissolve the raspberry gelatin completely in the boiling water, then stir in the cold water. Slowly pour the gelatin evenly over the cake, concentrating on the holes so the raspberry mixture can seep throughout the cake.
Warm the raspberry preserves in a microwave-safe bowl for about 20–30 seconds, just until they become easy to spread. Spoon the preserves over the cake and gently spread them into an even layer.
Spread the thawed whipped topping evenly over the raspberry preserves. Sprinkle the shredded coconut generously over the entire surface.
Cover the cake and refrigerate for at least 4 hours, preferably overnight, so the gelatin can fully set and the flavors can meld. Garnish with fresh raspberries just before slicing and serving.
