Correct Answer:
A. 64
The number series 1, 8, 4, 27, 9, ______ follows an alternating pattern of squares and cubes. The numbers in the odd positions (1st, 3rd, 5th) are squares: 1 (1²), 4 (2²), 9 (3²). The numbers in the even positions (2nd, 4th) are cubes: 8 (2³), 27 (3³). Following this pattern, the next number in the series, which is in the 6th position, should be the next cube, which is 4³. Therefore, 64 (Option A) is the correct answer. Options B and C do not follow the established pattern.