In a bowl, toss the fruitcake in the rum and let it stand for 10 minutes.
In each of six 6-ounce parfait glasses, make layers of the softened ice cream and the fruitcake mixture, beginning with a layer of ice cream and ending with a layer of fruitcake.
Freeze the filled parfait glasses, covering loosely, for at least 30 minutes and up to 24 hours. (Note: If freezing for longer than 2 hours, let the parfaits stand at room temperature for 5 to 10 minutes to soften slightly before serving.
Just before serving, in a chilled bowl, beat the cream until it just holds stiff peaks, transfer it to a pastry bag fitted with a decorative tip and pipe it onto the parfaits.
Garnish the parfaits with candied fruit, if desired.