In the bowl of a stand mixer fitted with a paddle attachments, beat the cake mix, instant pudding, eggs, water, oil, cinnamon and 1/2 cup of the sour cream on low until well combined. Using a flexible rubber spatula, fold in the apples.
Pour the cake batter into a greased and floured 10-inch tube pan. Bake until a cake tester comes out clean, about 1 hour. Cool the cake in its pan for 15 minutes. Run an offset spatula along the sides of the cake to loosen it from the pan.
Carefully invert the cake onto a wire rack. Remove the pan, and allow the cake to cool completely.
In a small bowl, whisk the sugar, 1 teaspoon of water, and the remaining 2 tablespoons of sour cream until well-blended.
Drizzle the icing over the cake. Let stand until the glaze is firm, then serve.
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