Preheat the oven to 350º F (180ºC). Like the bottoms of two 6-inch round cake pans with parchment paper circles. Grease and flour the insides.
Purée the berries in a blender or small food processor. Strain the puréed berries through a sieve. Reserve 2/3 cup (150g) of the berry puree. Set aside the remaining puree for the syrup.
In a medium-size bowl, whisk together the flour, baking powder, baking soda, and salt until well combined.
In a large bowl, beat 1 1/4 cups (250g) of sugar with the oil, eggs and vanilla extract, with an electric mixer on medium speed, until light and fluffy. Stir in the reserved 2/3 cup berry purée. Add the flour mixture in two additions, alternating with the buttermilk, beating at low speed just until combined.
Pour the batter evenly into the prepared cake pans. Bake until a toothpick inserted into center of cakes comes out clean, about 30-35 minutes. Cool the cakes in the pans for 10 minutes. Remove the cakes from pans and transfer them to cooling racks to cool.
While the cakes are baking, make the berry syrup. In a small saucepan, heat the remaining berry purée with the remaining 1/4 cup sugar (50g) and 1/4 cup (59ml) of water over medium-low heat. Stir together and cook until sugar is dissolved. Set aside to cool.
Split each cooled cake llayer into two and brush with berry syrup. Fill and frost the cake with Silky Cream Cheese Frosting.