Move oven rack to lowest position. Preheat oven to 350 degrees F.
Combine the water, Mexican coffee flavored liqueur, and instant coffee in a medium mixing bowl. Stir until coffee crystals have dissolved.
Add cake mix and cocoa powder and using an electric hand mixer, beat on low speed for 30 seconds; then beat on medium speed for 1 minute. Pour into an ungreased 10 by 4-inch tube pan. Bake in preheated oven for 37 to 47 minutes or until top is a dark golden brown, cracked, and not sticky.
Remove from oven and immediately turn pan upside down onto a bottle until cooled completely. Run knife around edges of pan and remove cake from pan.
For the icing: Whisk together all ingredients in a medium mixing bowl until smooth. Pour icing evenly over the top of the cake letting it run down the sides of the cake. Let icing set for 1 hour. Slice cake and serve garnished with orange zest.