Preheat the oven to 400 °F (204 °C). Lightly grease a donut pan and set aside.
In a large bowl, whisk together the sugar, brown sugar, and vegetable oil. Add the egg and whisk to combine.
1/4 cup granulated sugar, 3 tablespoons light brown sugar, 1/4 cup vegetable oil, 1 egg
Whisk together the flour and baking powder then add half the flour mixture to the bowl with the sugar. Stir to incorporate.
1 1/3 cup all-purpose flour, 1 teaspoon baking powder
Pour the milk and mix. Finally, add the remaining flour and incorporate until there is no longer any flour visible.
1/2 cup milk
Add the raspberries and carefully fold them in and try not to burst or break them.
⅔ cup fresh raspberries
Spoon the batter into the prepared donut pan, about 3/4 full. Bake for 10 minutes or until golden brown and baked through. Remove from the oven and let it cool completely before removing from the pan.
While the cake donuts are cooling, prepare the glaze. In a bowl whisk together all the ingredients until shiny and reaching a consistency you like. I prefer a thicker glaze for this.
1 cup confectioners sugar, 2 tablespoons heavy cream, 1 tablespoon lemon juice
Once the donuts have cooled completely, dip the top of each donut in the glaze. Before the glaze sets, sprinkle chopped freeze-dried raspberries for visual appeal, if desired. Allow to set before serving.