Preheat oven to 350°.
Beat 1 1/2 cups sugar, cream cheese, butter, and vanilla at medium speed of a mixer until well-blended (about 4 minutes). Add eggs, 1 at a time, beating well after each addition; set aside.
Lightly spoon flour into dry measuring cups; level with a knife. Combine the flour, baking powder, and salt. Add flour mixture to creamed mixture, and beat at low speed until blended. Combine 1/4 cup sugar and cinnamon. Combine 2 tablespoons of the cinnamon mixture and apple in a bowl; stir apple mixture into batter. Pour batter into an 8-inch springform pan coated with cooking spray, and sprinkle with remaining cinnamon mixture.
Bake at 350° for 1 hour and 15 minutes or until cake pulls away from the sides of pan. Cool cake completely on a wire rack, and cut using a serrated knife.
Note: You can also make this cake in a 9-inch square cake pan or a 9-inch springform pan; just reduce the baking time by 5 minutes.