Prepare the Pudding Mixture:
In a large bowl, beat the softened cream cheese and dry vanilla pudding mixes with a mixer until well blended.
Gradually beat in the milk until smooth.
Gently fold in the Cool Whip (reserving 1/2 cup for the final layer).
Assemble the Cake:
Spread a thin layer of Cool Whip in the bottom of a 9×13-inch pan to lightly coat it.
Arrange 5 graham crackers across the center of the pan, then break 2 more to fit around the edges.
Spread a layer of the pudding mixture over the graham crackers, followed by a layer of sliced strawberries and blueberries.
Add another layer of graham crackers on top of the berries, followed by more pudding mixture and another layer of berries.
Repeat this process one more time (3 total layers of graham crackers, pudding mixture, and berries) until the pan is filled.
Chill the Cake:
Cover and refrigerate the icebox cake for at least 4 hours, or overnight, to allow the graham crackers to soften and absorb the flavors.
Add White Chocolate Drizzle:
When ready to serve, melt the white chocolate chips according to package directions.
Drizzle the melted chocolate over the top of the cake. You can use a spoon or transfer the melted chocolate to a zip-top bag, snip the corner, and pipe it over the top of the berries.
Serve:
Slice and serve the chilled Summer Berry Icebox Cake for a refreshing no-bake dessert perfect for warm weather!