Stir water and sugar in a saucepan over a low heat until sugar has completely dissolved. Bring sugar syrup to a boil over medium heat, stirring frequently. Remove from heat and allow to cool in fridge for 30 minutes.
Puree mango flesh in food processor or blender until smooth. Set mango puree aside.
Stir together mango puree, cooled sugar syrup and white rum.
Prepare the mango rum sorbet using an ice cream make according to your ice cream maker's instructions.
Pour into a container and freeze until solid.