Clean, wash, halve and stone the plums. Cut the flesh into small pieces. Cream butter and sugar with the whisk of the hand mixer. Stir in eggs one by one. Mix flour and baking powder. Mix sour cream and 50 ml syrup. Alternately stir in the flour and cream mixture briefly.
Mix plums and 2 tablespoons ground hazelnuts and fold into the dough. Pour into a greased box form (26 cm long) sprinkled with the remaining ground hazelnuts. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for 50-60 minutes. Leave the cake to cool slightly while still in the tin. Turn out, soak with 50 ml syrup and allow to cool completely. Stir the lilac berry juice and icing sugar until smooth. Coat the cake with this and let it dry