Ask a Marine, Navy Seal, or Ranger. These guys have bodies of steel and are well known for incredible feats of endurance as well as strength. There is more BS about nutrition in bodybuilding/powerlifting than I have seen in any other sport. Just keep a steady and adequate supply of carbs going during your rides and a post-workout meal of clean protein and complex carbs to rebuild and refuel, and you won't have any trouble building both endurance and strength. While cyclists aren't known for massive biceps, take a look at the quads and calves on the pros. Holy muscle mass, Batman.

Just remember that if you add a mass building routine to your workouts, you will have to make appropriate adjustments to your recovery and nutrition to support the combined program.