Three dice are thrown. The probability of getting a sum of numbers which is a perfect cube, is:

$\frac{7}{72}$

If three dice are thrown together, sample space =

{(111), (112).....(166)

  (211),...............(266)

  (311),...............(366)

  (411),...............(466)

  (511),...............(566)

  (611),...............(666)}

Total number of outcomes = 216

Minimum sum of the three outcomes = 3

Maximum sum of the three outcomes = 18

Perfect cubes in 3 to 18 = 8

Chances of getting the sum as 8 = (116)(161)(611)(125)(152)(215)(251)(521)(512)(134)(143)(413)(431)(314)(341)(224)(242)(422)(332)(232)(233)

Required probability = 21/216 = 7/72

The correct answer is Option (4) → $\frac{7}{72}$