Puree the berries in a blender or food processor. Dissolve the cornstarch in the liqueurs 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. Serve with fondue forks or metal or wooden skewers so that diners can dip their choice of fruit or cake into the sauce.