Preheat the oven 350 degrees F. Spray a 10-cup Bundt pan with cooking spray.
Whisk the cake mix, pudding mix, coconut oil, coconut extract, egg whites and 3/4 cup water in a large bowl until completely smooth. Pour into the prepared bundt pan and bake until the top is golden brown and a toothpick inserted in the center comes out clean, about 35 minutes. Let cool in the pan for 10 minutes. Flip the cake out onto a wire rack and place the rack over a baking sheet; let cool completely, about 1 hour. Trim the bottom of the cake with a serrated knife so it will sit flat on a serving platter.
Put the chocolate in a medium heat-safe bowl. Put the cream in a medium microwave-safe bowl and microwave until boiling, about 2 minutes. Pour the hot cream over the chocolate and let stand for 5 minutes. Stir until completely smooth. Refrigerate until cooled, about 20 minutes.
Pour the ganache over the cake, making sure to cover the cake completely and letting any excess drip down into the baking sheet beneath the rack. Cover the top and sides with 1 cup of the coconut. Refrigerate until the chocolate is hardened, about 30 minutes.
Meanwhile, put the mangoes in a blender and puree until smooth. Pour 1 1/2 cups puree into a small saucepan (reserve any leftover puree for another use).
Stir the sugar into the saucepan with the puree and bring to a boil over medium-high heat. Cook, stirring occasionally, until the sugar is dissolved, about 3 minutes. Whisk the cornstarch with 1 1/2 teaspoons water in a small bowl until smooth. Pour into the mango mixture and cook until slightly thickened, about 1 minute. Transfer to a small bowl and let cool at room temperature, about 20 minutes.
Transfer the cake to a serving platter. Pour the mango puree into the hole in the center of the cake, letting it come all the way up to the top but not dripping over the sides. Sprinkle the remaining 1/4 cup coconut on top of the mango puree to cover it completely. Slice the cake, pull out a piece and watch the mango ooze out.
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