Place rack in center of oven, and preheat oven to 350. Grease and lightly flour inside of 10 inch bundt pan.
Whisk together flour, baking powder, baking soda and salt in a large bowl. Set aside.
Using either a stand mixer (paddle attachment) or a hand mixer, beat the butter at medium speed until creamy, about 2 minutes. Gradually add 1 3/4 cup of sugar and beat at medium-high speed until the mixture is light in texture and color, about 3 minutes. Beat in eggs one at a time, beating for 30 to 40 seconds after each addition. Scrape down sides of bowl as necessary. At low speed, add flour mixture in three additions, alternating with sour cream. (Add a bit of flour, a bit of sour cream, a bit of flour, a bit of sour cream, a bit of flour.)
Scoop half of batter into pan and spread with spatula. Sprinkle with peaches. Scoop remaining half of batter on top of peaches. Smooth with spatula.
Bake cake for 50 to 60 minutes, or until a tooth pick inserted in the center comes out clean. Cool the cake in the pan on a cooling rack for 10 minutes, then invert it onto another rack. Place the cake, on the rack, over a baking sheet.
While cake is baking, make syrup. Combine peach puree, 2/3 cups of sugar, and orange juice in a small non reactive saucepan and cook over medium heat, stirring until the sugar dissolves, 3 to 4 minutes. Remove pan from heat. Using a pastry brush, dab syrup generously all over surface of the warm cake, allowing it to soak into the cake before reapplying. Let the cake cool completely.