The cube of a number is obtained by multyplying the given number three times. In the given number, that is, (2*2*3*3*3), the number 2 is present two times and the number 3 is present three times. Accordingly, to obtain a perfect cube the given number will be multiplied by 2. The resulting number will be (2*2*2*3*3*3) which is 216. 216 is the perfect cube of 6.