Combine water and cinnamon sticks in a medium saucepan over high heat.
Bring to a boil. Reduce heat, cover, and simmer until cinnamon releases its color and flavor, about 5 minutes.
Add rice and bring to a boil. Reduce heat, cover, and simmer until rice is tender and water is absorbed, about 20 minutes.
Stir in whole milk, evaporated milk, and sweetened condensed milk. Cook uncovered over medium heat until mixture has thickened to desired consistency, 15 to 20 minutes.
Serve warm or cold. Sprinkle each portion with ground cinnamon.