Line a 9-by-13-inch baking dish with plastic wrap. Place half the baked angel food cake in bottom of dish. Spread jam over top. Spread ice cream over jam. Freeze until firm, about 1 hour.
Spread raspberry sorbet over ice cream layer. Freeze until firm, about 2 hours. Spread peach sorbet over raspberry layer; top with remaining angel food cake. Wrap in plastic wrap; freeze overnight.
Remove plastic from top of cake, and turn out cake onto a cutting board; unwrap, and trim edges. Slice cake, and serve immediately.
Uncut cake can be frozen for up to 1 week.