In the bowl of a stand mixer with a paddle attachment, combine the cream cheese and granulated sugar. Beat on medium-high for 1 to 2 minutes until smooth. Scrape the sides and bottom of the bowl. With the mixer on medium, slowly add the heavy cream and mix until combined. Switch to the whisk attachment and whip at medium speed until soft peaks form and the mixture is easy to dollop. In a large trifle dish (about 12 to 14 cups), place a single layer of cake cubes. Top with two-thirds of the blueberries and blackberries, then one-half of the whipped cream (about 2 cups), then two-thirds of the strawberries. Repeat the cake and cream layers once more, then decorate the top with the remaining berries. Serve immediately or make in advance and store for up to 24 hours in the refrigerator.