Preheat oven to 325. Grease and flour bundt pan.
Whisk 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.
Beat egg whites in a large bowl on high speed until light and foamy. gradually beat in 1/2 c. sugaruntil stiff glossy peaks form.
Beat butter and cream cheese in a large bowl until creamy. Add remaining 1 1/2 c sugar and beat, scraping down sides of bowl, as needed, untilpale and fluffy, about 4 minutes. Alternetly add the flour and buttermilk mixtures, beating until just smooth. fold in about 1/3 egg whites wiht a rubber spatula until just smooth and no white streaks remain. Fold in remaining egg whites, scrape the batter inot the prepared pan, spreading evenly.
Bake the cake until it tests done; about 1 hr
Cool in pan 10 minutes; loosen edges with a knife and turn out of pan. Let cool at least 1 hour before slicing.