Put both juices and sugar in a saucepan and simmer, stirring until sugar dissolves. Pour gelatin (prepared according to package instructions), cook to a boil, remove from heat and strain.
Grind strawberries in a food processor. Stir in the strawberry puree to the mixture, allow to cool slightly and pour into a mold. Refrigerate several hours or overnight , until set.
Using a corer, remove balls of melon pulp. Pour the mold onto a serving plate, fill the center of the pudding with melon balls and serve.