In a medium saucepan over medium-high heat, bring the sugar and water to a boil, stirring occasionally.
Boil until the sugar has dissolved and the syrup is clear, 2 to 3 minutes.
Immediately place the pan in the ice water and let it cool, stirring occasionally, until the sugar syrup is at room temperature.
Peel and dice the mangoes, discarding the pits. Process the mango along with the lime or lemon juice and the sugar syrup in a blender or food processor and process until smooth. Transfer the mixture to a container and stir in the cream.
Cover and refrigerate until thoroughly chilled, about 3 hours.
Freeze the mixture in an ice cream maker according to the manufacturer’s instructions, probably 20 to 30 minutes.
Transfer to a resealable container, cover, and freeze until firm, about 2 hours. Scoop into bowls and serve.