Heat oven to 350° F. Grease 12-cup fluted tube cake pan with shortening or cooking spray.
Cut block of cream cheese into 24 equal-sized cubes. (Start by first halving block so that you have 2 thin pieces, and then cut each thin half into 12 equal squares.)
Set aside icing from cinnamon rolls. Separate each can of dough into 5 rolls; unroll each roll, and cut each in half.
Take a section of dough and fold it over so you have a rectangle shape that is 1 layer of dough thick. Place a square of cream cheese in the dough; fold over the dough, and gently crimp it around the cream cheese. Repeat with remaining dough pieces.
Place cream cheese-filled dough balls in pan. Place butter pieces on top.
Bake 40 to 45 minutes or until golden brown across top. Cool 10 minutes; run knife around edge of pan to loosen. Place heatproof serving plate over pan and turn over; remove pan. Cool 10 minutes longer.
Drizzle reserved icing over top of bread, allowing some to drizzle down side. Pull apart to serve; serve warm.