Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
Add the softened butter to the dry ingredients and mix on medium speed until the mixture is crumbly and well combined.
In a separate bowl, beat the eggs and then add the vanilla extract and buttermilk. Mix until smooth.
Gradually add the wet ingredients to the dry mixture, mixing until just combined. Be careful not to overmix.
Gently fold in the black raspberries, being careful not to break them apart too much.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.