The sequence presented is intriguing as it appears to be a combination of perfect cubes and perfect squares. To analyze the pattern more closely, we can take a look at these numbers:
- 1 = 13 (perfect cube)
- 4 = 22 (perfect square)
- 27 = 33 (perfect cube)
- 16 = 42 (perfect square)
- 125 = 53 (perfect cube)
- 36 = 62 (perfect square)
From this breakdown, it becomes clear that the sequence alternates between perfect cubes and perfect squares:
- 1 (3rd power) – follows 4 (2nd power)
- 27 (3rd power) – follows 16 (2nd power)
- 125 (3rd power) – follows 36 (2nd power)
Continuing this pattern, the next number would be the cube of 6, since the previous cube was 125 (which is 53):
- 63 = 216
Thus, the next number in the sequence is 216.