Brush a box form (11 x 25 cm; 1.25 litre capacity) with oil, line it with baking paper and place it in the freezer.
Let the strawberry ice cream thaw for about 15 minutes. Sort the raspberries. Crush about half of the raspberries and icing sugar with a fork. Put the strawberry ice cream into a mixing bowl and stir until soft with the dough hooks of the hand mixer.
Stir in crushed raspberries. Pour ice into the box mould, smooth it down and freeze for about 2 hours.
Stir the jam until smooth and spread on the strawberry ice cream. Freeze for about 1 hour. Let vanilla ice cream thaw for about 15 minutes. Pour vanilla ice cream into a bowl and stir until soft using the dough hooks. Pour onto the jam and smooth it down.
Cut the sponge cake into a rectangle of about 11 x 25 cm and place it on the vanilla ice cream. Freeze for about 3 hours. Use the remaining sponge cake for other purposes.
Select the strawberries and blueberries, wash and drain well. Clean and chop the strawberries. Turn out the ice-cream cake from the mould, place it on a plate, remove the baking paper and decorate the ice-cream cake with strawberries, raspberries and blueberries.
Crumble cookies and spread them on top.