Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a mixing bowl, combine the mashed sweet potatoes, cake mix, pudding mix, eggs, oil, milk, vanilla, cinnamon, and nutmeg. Mix until smooth.
In a separate bowl, mix the brown sugar and ground cinnamon for the swirl.
Pour half of the cake batter into the prepared pan. Sprinkle half of the cinnamon mixture over it. Pour the remaining batter and top with the rest of the cinnamon mixture.
Bake for 45 minutes or until a toothpick comes out clean.
For the glaze, mix powdered sugar, milk, and vanilla in a bowl until smooth. Drizzle over the cake once it has cooled.
Notes
This cake can be served warm or at room temperature. Store leftovers in an airtight container.