Preheat oven to 350 degrees. Butter and flour a bundt pan.
Whisk flour, almond meal, baking powder, baking soda and salt. Set aside.
Working with a stand mixer with paddle attachment, beat the butter and brown sugar on high speed until light and fluffy.
Add eggs one at a time beating just to incorporate. Add the vanilla, almond paste and almond extract and beat to combine. Reduce mixer speed to low and add flour mixture and buttermilk alternately, beginning and ending with the dry ingredients. Stop mixing as soon as the flour is incorporated. Gently fold in blackberries. Spoon the batter into the prepared pan and lightly smooth the top with a rubber spatula.
Bake for 60 to 65 minutes until a cake tester inserted in thickest part of cake comes out clean. If the top starts to turn dark brown during baking, cover the cake with foil and return to the oven to finish baking.
Transfer to a cooling rack for 10 minutes and then unmold. Serve dusted with powdered sugar.