Preheat oven to 325° F. Coat a 12-cup Bundt pan with cooking spray and dust with flour.
Whisk all-purpose flour, whole-wheat flour, baking powder and salt in a medium bowl. Whisk whole eggs, buttermilk, oil, corn syrup and vanilla in another medium bowl until well blended.eat egg whites in a large clean bowl with an electric mixer on high speed until light and foamy. Gradually beat in 1/2 cup sugar until stiff glossy peaks form.eat butter and Neufchatel in a large bowl until creamy. Add the remaining 1 1/2 cups sugar and beat, scraping down the sides of the bowl as needed, until pale and fluffy, about 4 minutes. Alternately add the flour and buttermilk mixtures, beating until just smooth. Fold in about one-third of the egg whites with a rubber spatula until just smooth and no white streaks remain. Fold in the remaining egg whites. Scrape the batter into the prepared pan, spreading evenly. e the cake until a wooden skewer inserted into it comes out clean and the top springs back when touched, 1 hour to 1 hour 10 minutes. Cool in the pan on a wire rack for 10 minutes. Loosen the edges with a knife and turn out onto the rack; let cool for at least 1 hour more before slicing.