Mix citrus juices in small saucepan. Sprinkle gelatin over. Let stand 10 minutes. Stir over low heat until gelatin dissolves. Let stand until just cool but not set.
Combine mango, sour cream, milk, sugar and rum in blender. Blend on high speed until smooth. Add gelatin mixture and blend well. Pour into six 6-ounce souffle dishes or custard cups. Divide berries among dishes; press berries into puddings. Cover with plastic wrap and chill until firm (at least 5 hours or overnight.)