For the Cake:

1. Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.
2. In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
3. In a large bowl, cream together butter and sugar until light and fluffy (about 3-4 minutes).
4. Add eggs one at a time, mixing well after each addition. Stir in vanilla extract, lemon zest, and lemon juice.
5. Alternate adding the dry ingredients and buttermilk to the butter mixture, starting and ending with the dry ingredients. Mix until just combined.
6. Gently fold in the mashed blackberries.
7. Divide the batter evenly between the prepared pans. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
8. Let cakes cool in pans for 10 minutes, then transfer to a wire rack to cool completely.

For the Blackberry Frosting:

1. In a small saucepan, heat blackberries over medium heat until they break down (about 5 minutes). Mash, strain through a fine mesh sieve to remove seeds, and let cool.
2. In a large bowl, beat butter and powdered sugar until creamy.
3. Add blackberry puree, heavy cream, vanilla extract, and salt. Beat until fluffy.
4. Spread frosting over one cake layer, place the second layer on top, and frost the top and sides. Decorate with fresh blackberries if desired.