In a 4-quart saucepan, cook the strawberries, jelly and sugar over medium heat, stirring until melted and bubbling, about 2 minutes. Add raspberries and crème de cassis, raise the heat to med-hi and bring to a simmer. Simmer, stirring constantly, until most of the fruit has broken down and the sauce is slightly thickened, about 10 minutes. Set aside to cool 10 minutes.
Line a 2-quart high-sided round soufflé or baking dish with plastic wrap.
Pour 1 cup of the berry mixture over the bottom of the prepared dish. Cut or tear 2-3 pieces of bread and fit into the dish, gently nestling them in a single layer into the berry mixture. Repeat with alternating layers of bread and berries, tearing or cutting each layer of bread to fit. End with a thin coating of berries on top.
Cover with plastic overhang and place a small plate on top of the plastic. Place a large can on top of the plate and refrigerate 18-24 hours.
Just before serving, remove the can and plate from the pudding mixture and peel back the plastic wrap. Invert the pudding onto a serving platter and remove dish. Peel off the plastic wrap. To serve: slice into wedges and serve with a scoop of ice cream and extra berries for garnish.