In a 2 1/2-quart glass bowl, arrange half the cake pieces.
Stir together pudding mix and milk according to package directions. Fold in whipped topping and vanilla.
Top cake pieces with half pudding mixture. Top with 1/2 cup each strawberries and blueberries. Repeat layers (cake, pudding, fruit).
Cover. Chill for 8 hours. Serve.