1. Trim crust off cake. From bottom, horizontally cut four 1/2-inch-thick slices. Spread each with 2 tablespoons jam; stack. Cut in half lengthwise, then crosswise into eighths.
2. Grease 9-inch springform pan. Arrange cake stacks against side of pan around base; stand on edge so jam lines are vertical; place stacks, jam edge to plain edge. Crumble remaining cake into center. Using waxed paper, press firmly in even layer. Remove paper; gently spread remaining jam over cake layer. Refrigerate. (Can be made 2 days ahead; refrigerate.)
3. Soften gelatin in 1/2 cup water in small saucepan, 5 minutes. Heat, stirring, until gelatin has dissolved.
4. Puree mangos, liqueur, ginger and 1/4 cup of the sugar in processor. Transfer to bowl; add gelatin. Chill, stirring often, until thick like egg whites.
5. Beat powdered whites and 6 tablespoons water in bowl to form soft peaks. Gradually beat in remaining 1/2 cup sugar to form stiff peaks. Fold into mango mixture. Fold in whipped cream. Scrape into prepared pan. Chill 5 hours or overnight to set.