Preheat the oven to 350°F. Grease a 12-cup bundt pan with cooking spray or shortening.
Open the cans of biscuits and cut each biscuit into 4 pieces. With both cans of 8 biscuits each, that is a total of 64 cut pieces.
Into a large plastic bag, pour in 1/2 cup white sugar and the cinnamon. Working in batches, place the biscuit pieces in the bag and shake to coat with the cinnamon and sugar mixture. Transfer the coated pieces to the greased bundt pan.
As the coated biscuit pieces are placed in the bundt pan, place blueberries on top and in-between the biscuit pieces. When all have been transferred to the pan, pour any remaining sugar mixture over the top of the biscuits and also place any remaining blueberries on top.
In a microwave safe cup or bowl, melt the entire stick of butter. Remove from the microwave and add the remaining white sugar, brown sugar, and vanilla. Stir until smooth. Pour the butter mixture evenly over the biscuits and blueberries in the pan.
Bake on the middle rack of oven for 40 to 45 minutes, until the top is browned and the biscuits in the center of the pan feel firm to the touch. Place on a cooling rack for 10 minutes then invert onto a large plate. The berries will be hot. Allow to cool slightly before serving. Cut and serve warm.