Heat oven to 325 degrees. Butter and flour a 12-cup Bundt cake pan, or spray with a baking spray. Drain syrup from peaches; measure 1/3 cup of the syrup and reserve. Chop 1 29-ounce can sliced peaches finely and set aside.
Beat 1 cup unsalted butter and 2 1/2 cups granulated sugar until light and fluffy. Add 6 eggs, one at a time, beating after each addition. Beat in 2 tsps vanilla extract.
In another bowl, combine 3 cups all-purpose flour, 1 tsp baking powder, 1/2 tsp salt, and 1/4 tsp baking soda. Blend dry mixture into the creamed mixture. alternating with 1/2 cup buttermilk; fold in reserved 1/3 cup reserved peach syrup and the chopped peaches. Spoon into prepared baking pan. Bake for 1 hour to 1 hour and 15 minutes, or until a toothpick or cake tester comes out clean when inserted in center.
Cool in pan on a rack for 15 minutes. Invert the cake on the rack to cool completely. Put the baking pan over the cooled cake (matching the grooves and pattern) and flip with the rack. Then put a serving plate over the cake and invert again.