Preheat oven to 400 degrees F (205 degrees C). Grease and flour a 10-cup bundt pan. Set aside.
Using a stand or hand mixer, beat the butter and sugar in a large bowl until light and fluffy. The mixture will be very pale. Add eggs one at a time, incorporating each one before adding the next. Mix in the vanilla extract and maple extract/flavoring.
Combine the sour cream and pumpkin together in a measuring cup.
Combine the flour, baking soda, and baking powder in a medium bowl. Mix the flour mixture into the cake batter alternately with the 1 cup of sour cream/pumpkin mixture. End with the dry ingredients. Spoon half the batter into the prepared bundt pan.
Carefully spoon the cheesecake filling over the batter in the bundt pan, trying to keep away from the sides. Spoon the remaining cake batter over the cheesecake filling. Swirl through the batter once or twice with a knife if desired.
Bake in the 400 degree F (205 degree C) oven for 8 minutes. Then, lower the oven temperature to 350 degrees F (175 degrees C) and bake for 40 minutes more, or until a tester comes out clean.
Let the cake cool on a rack for 10-15 minutes before tipping the cake out of the pan onto a wire rack. Allow to cool completely before frosting.