Preheat the oven to 350F. Butter a deep (3 inches would be best) 9-inch round cake pan, and line the bottom with a circle of parchment.
In a large bowl, beat the butter and sugar until light and fluffy, then beat in the eggs one at a time, beating after each addition. Fold in the almonds, cold mashed potato, lemon zest and baking powder. Gently stir in the berries.
Tip the batter into the pan and spread it evenly over the bottom. Smooth the top. Bake for 40-45 mins or until golden and springy to the touch.
Let the cake cool completely, then dust with powdered sugar before serving.