In a small saucepan combine sugar, corn syrup, water, and cream of tartar. Over medium-high heat, cook sugar mixture until it reaches a temperature of 300 degrees F. Remove from heat. When mixture has cooled to 260 to 270 degrees F, stir in colorings and flavoring.
Cover the back of a baking pan with nonstick aluminum foil and arrange lollipop sticks 3 to 4 inches apart. Carefully spoon or pour sugar mixture over the end of lollipop sticks. If mixture becomes too thick, place pan over low heat and stir constantly until it loosens up. Let lollipops cool completely before touching. If you plan on keeping lollipops for more than a day, wrap individually in cellophane pouches.
When making candy, melted sugar becomes very hot. Please use extreme caution when handling an pouring. Licorice flavoring can be found where candy making and cake decorating supplies are sold.