Sprinkle nuts in well-greased 16 cup fluted tube dish.
In large bowl, with electric mixer, combine cake mix, pudding mix, eggs, water, oil and rum; beat at medium speed 4 minutes.
Pour batter evenly over nuts.
Cook at LOW 10 minutes and at MEDIUM-HIGH 6 to 8 minutes or until toothpick inserted near center comes out clean.
To dry top of cake, cover with wax paper last 2 minutes of cooking.
Let stand, uncovered, 15 minutes.
Meanwhile, in 2-cup glass measure combine butter, sugar and water; mix well.
Cook at HIGH 2 to 2 1/2 minutes; stir in rum.
Prick top of cake; drizzle half of Rum Glaze over cake (to absorb).
Invert cake onto serving platter and prick top and sides of cake; drizzle cake with remaining glaze.
Store, covered, until ready to serve.