Justin is mixing punch for his birthday party. his recipe calls for 2 1/2 cups of cranberry juice and serves 12 people. using the recipe, how many more cups of cranberry juice are needed to make punch for 18 people than are needed to make punch for 12 people?

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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