Preheat the oven to 350° F and spray 2 9” baking pans with baking spray or line with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium speed for 1 minute until fluffy and pale yellow in color.
Add in the eggs one at a time, stopping the mixer before each addition. You may have to scrape down the sides-stop the mixer.
In a medium size bowl combine the flour, baking powder, baking soda and salt.
In a large mixing cup or a small bowl, combine the yogurt and juice.
Add in ⅓ of the flour mixture, and mix on low until incorporated into the mix. Then add in ½ of the yogurt and juice mixture (while still on low). Then another ⅓ of the flour, the last of the juice, and the last of the flour mixture. Stopping to scrape down the sides as needed.
Toss the blackberries with 2 tablespoons of flour so they don’t sink to the bottom of your cake, and CAREFULLY mix them slowly into the batter. You don’t want to break them up so be careful with mixing.
Pour the batter evenly into the two baking pans and bake for 30-35 minutes until the edges of the cake are golden brown and break away from the pan- or when the top of the cake feels firm and not jiggly.