Using an electric mixer, cream together the eggs, white sugar and brown sugar in a large bowl. Add the oil, vanilla extract and the pumpkin puree and continue to beat until fully combined.
In a separate medium bowl, whisk the dry ingredients (flour, baking soda, baking powder, salt, and pumpkin spice). Add dry ingredients to wet ingredients and mix just until combined.
Carefully pour the batter into the bundt pan. Bake for 50-60 minutes or until a toothpick comes out clean. Remove from oven and set aside to cool on wire rack for about 30 minutes.