Preheat an oven to 350°F. Butter 2 round 8-inch cake pans, line the bottoms with parchment paper, and butter that as well. Set aside.
Shuck the corn. Using the large holes on a grater, grate the kernels into a medium bowl (this method gets more of the kernel from the cob than simply cutting them). Whirl in a blender with the milk and vanilla.
In a small bowl, combine the flour, baking powder, and salt. Set aside.
In a large bowl or the bowl of a standing mixer, beat the butter, oil, and sugar until light-looking and fluffy. Separate the eggs. Add the yolks, one at a time, to the butter mixture, beating for 30 seconds after each addition.
Beat in the corn mixture, then stir in the flour mixture just enough to combine everything (don’t overbeat).
In a large bowl, beat the egg whites until they hold soft peaks—the beaters should pull up a peak of whites when lifted from the bowl, but that peak should droop back down. Stir about ⅓ of the whites into the batter, then fold in the remaining whites.
Pour the batter into the prepared pans and bake until a toothpick inserted in the center comes out clean, about 30 minutes. Let the cake cool on a rack.
Whip the cream and sugar to hold soft peaks, use to “ice” the cake, adding berries to each layer.