In a saucepan bring sugar, 1-1/2 cups water, and corn syrup to a boil, stirring until sugar is dissolved. Remove pan from heat and cool. In a metal bowl set over a pan of barely simmering water melt chocolate, stirring, and cool. In a bowl whisk together cocoa powder and syrup mixture and add melted chocolate and rum, whisking until smooth. Whisk in remaining 2 cups water and strain through a fine sieve into a bowl. Freeze sorbet in an ice-cream maker. Sorbet may be made 1 week ahead. Makes about 5 cups.