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Option 3 : 64

Series A: 1, 4, 9... is square of numbers 1,2 and 3....

Series B: 1, 8, 27...is cube of numbers 1, 2 and 3.....

Thus the only number that is a perfect square of a number and a perfect cube of another number will fit both the series.

42 is neither a square nor a cube of any whole number. 36 is square of 6 but not a cube. Similarly, 25 is square of 5 but cube of none. Option 64 is square of 8 and cube of 4.

Hence the required number is 64.
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