In medium bowl, mix together mango fruit pulp, sugar, ½ cup water, lemon juice and cayenne pepper, stirring until sugar dissolves.
Evenly divide mango cubes among eight 3-oz. ice pop molds. Pour mango pulp mixture into molds. Transfer molds to freezer; freeze until slushy, about 1 hour. Insert Popsicle stick into each mold; freeze until pops are frozen solid, about 3 hours more.
To serve, quickly run bottom of molds under hot water before unmolding.
To make paletas, or ice pops, without store-bought ice pop molds, simply pour the mango mixture into small juice glasses or paper cups that hold at least 3 oz. each. Then, proceed with Step 2 of recipe.