Preheat oven to 350° F.
Spray a Bundt pan with baking spray. Set aside.
In a large bowl, beat butter and cream cheese at medium speed with a mixer until fluffy, 3 to 4 minutes.
Mix in 1 cup sugar and 1 cup brown sugar until incorporated, about another 3 minutes.
Add eggs, one at a time, beating well after each addition.
Add shredded sweet potato and vanilla, beating until combined.
In a medium bowl, whisk together flour and 1½ teaspoons pumpkin pie spice.
Gradually add flour mixture to sweet potato mixture, beating at low speed just until combined.
In a small bowl, stir together the remaining ⅓ cup sugar, remaining 1 tablespoon brown sugar, and remaining 1 tablespoon pumpkin pie spice.
Spoon ⅓ of the batter into the prepared pan (batter will be thick and a little sticky), spreading evenly.
Sprinkle half of the sugar-spice mixture over batter.
Repeat the process once and then top with the remaining batter.
Bake until an inserted toothpick near the center comes out clean, approximately 50 minutes.
Let cool in the pan for 10 minutes.
Carefully remove the cake from the pan and let cool completely on a wire rack.