Puree the berries in a blender or food processor. In a small bowl, dissolve the cornstarch in the liqueur or water. Place the pureed berries and the cornstarch mixture in a small saucepan and heat over medium heat, stirring frequently, until the mixture thickens slightly and the milky color has disappeared. Pour into a serving bowl or fondue pot. Serve with fondue forks or metal or wooden skewers so that diners can dip their choice of fruit or cake into the sauce.