Preheat oven to 350 degrees Fahrenheit. Grease a 9"x 13" baking pan with butter and dust with flour.
In a stand mixer fitted with the paddle attachment, beat the butter on medium speed until soft, about 2 minutes. Add the granulated sugar and continue to beat until well mixed and creamy, about another 5 minutes. One at a time, beat in the eggs on medium speed until completely smooth and creamy, about 2 minutes.
In a large bowl, combine the all-purpose flour, baking powder, baking soda and salt.
Put the diced mango, buttermilk, and almond and vanilla extracts in a blender, and puree until completely smooth.
In four additions, gradually beat the mango puree and the dry ingredients into the butter mixture, alternating wet and dry ingredients. Mix until completely combined. Scrape the batter into the greased and dusted baking pan and place in the oven. Bake for 30 minutes, or until the cake is golden brown on top, springy to the touch, and a wooden toothpick comes out dry when inserted.
Remove from the oven and let cool. Turn the cake out upside down onto a board, and then flip right side up onto a platter. Dust liberally with confectioners’ sugar before serving, and garnish with berries of your choice.