Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, whisk together flour, baking powder, baking soda, and salt.
In a separate bowl, cream together butter and sugar until light and fluffy. Beat in eggs one at a time, then stir in vanilla.
Gradually add the dry ingredients to the wet ingredients, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined.
Fold in the blueberries.
In a small bowl, beat together cream cheese, butter, and powdered sugar until smooth. Spread batter into the prepared pan, then dollop spoonfuls of the cream cheese mixture over the top. Swirl with a knife to create a marbled effect.
Bake for 35-40 minutes, or until a wooden skewer inserted into the center comes out clean.
Let cool completely before serving.
Notes
Store leftover cake in an airtight container at room temperature for up to 3 days.