Heat oven to 350°F. Grease 2 (6-cup) miniature fluted tube cake pans with shortening; lightly flour. In medium bowl, beat cake ingredients except chocolate chips with electric mixer on low speed 30 seconds. Beat on medium speed 2 minutes, until smooth. Stir in chocolate chips. Divide batter evenly among pans.
Bake 18 minutes or until toothpick inserted in center comes out clean. Cool 5 minutes. Carefully invert each pan onto cooling rack; lift pan from cakes. Cool completely, about 30 minutes.
Place bittersweet chocolate in medium bowl. In 1-quart saucepan, heat whipping cream to simmering; pour over chocolate. Let stand 3 minutes. Stir in 1 tablespoon rum. Spoon glaze over cakes.
In small resealable freezer plastic bag, place white chocolate; seal bag. Microwave on High about 1 minute or until softened. Gently squeeze bag until chocolate is smooth; cut off tiny corner of bag. Squeeze bag to drizzle chocolate over cakes.