Grind half of each type of berry in a hand mixer and spread through a sieve. Beat the yolks with the sugar until creamy, stir in the mascarpone and divide half of the mixture evenly between two baking bowls. Heat half of the coconut liqueur and let the soaked gelatine melt in the hot liqueur. Stir the pureed berries through with one half of the mascarpone cream. Fold half of the coconut liqueur-gelatin mixture into this part of the cream, the other half into the light part. Drizzle the remaining liqueur over the sponge cake bottoms.
Place springform pan rim on a baking sheet and place the first chocolate sponge cake layer. Brush half of the berry mascarpone cream and evenly spread half of the remaining blackberries and blueberries on top. Place second sponge cake layer on top. Brush 3/4 of the light cream and evenly distribute half of the raspberries on top. Place the third sponge cake layer on top. Remove springform rim, spread cake thickly all around with remaining berry mascarpone cream. Spread thick blobs of the light cream evenly on top, sprinkle coconut flakes on the sides and refrigerate.