Place eggs in a saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, cool, and peel. Place eggs in a glass or plastic container.
Combine beets, vinegar, sugar, water, and cinnamon in a saucepan. Bring to a boil; stir until sugar is dissolved. Pour over eggs.