1. Remove all unpopped kernels from popped popcorn. Place popcorn in a buttered 17x12x2-inch baking pan or roasting pan. Keep popcorn warm in a 300 degree F (150 C) oven while preparing marshmallow mixture.
2. In a large saucepan bring corn syrup and sugar to boiling over medium-high heat, stirring constantly. Remove from heat. Stir in marshmallow creme, butter, and vanilla until combined.
3. Pour marshmallow mixture over hot popcorn; stir gently to coat. Cool until popcorn mixture can be handled easily. Stir in candies. With damp hands, quickly shape mixture into 3-inch-diameter balls. Wrap each popcorn ball in plastic wrap. Store at room temperature up to 1 week.
Popcorn Cake: Turn popcorn mixture into a buttered 10-inch tube pan. Press gently into pan with spatula or damp hands. Let stand about 30 minutes; remove and slice like cake.