Cook together sugar with ten tbsps water in a non-stick pan, stirring till the sugar dissolves. Halve the cake horizontally. Dab the cake pieces with the sugar syrup on one side.
Place one half on a serving plate. Take one cup whipped cream in a bowl, add two tbsps strawberry puree and one tbsp rum and mix well. Spread this mixture over the moistened piece of the cake. Spread some of the strawberry pieces and two tbsps of grated chocolate over the cream.
Place the second half of the cake over this. Mix the remaining whipped cream with the remaining rum and mix well. Spread this on top of the second half of the cake. Sprinkle the remaining grated chocolate and the remaining strawberry pieces. Cut into wedges and serve.