In a 9- by 13-inch baking dish, mix blueberries and raspberries with 1/4 cup granulated sugar. Spread level.
In a bowl, whisk eggs, olive oil, orange peel, vanilla, and remaining 1 cup granulated sugar. Stir in flour, baking powder, and salt until just combined. Pour batter evenly over berry mixture and gently spread to cover berries.
Bake cake in a 350° regular or convection oven until top springs back slightly when gently pressed in the center, 28 to 35 minutes. Let cool at least 10 minutes; serve warm or cool. Sprinkle with powdered sugar just before serving, and scoop portions onto plates.