What is the next number in the sequence 1, 4, 27, 16, 125, 36?

The next number in the sequence is 49.

This sequence alternates between cubes of integers and perfect squares. Let’s break it down:

• The 1st number is 1, which is 1³ (1 cubed).
• The 2nd number is 4, which is 2² (2 squared).
• The 3rd number is 27, which is 3³ (3 cubed).
• The 4th number is 16, which is 4² (4 squared).
• The 5th number is 125, which is 5³ (5 cubed).
• The 6th number is 36, which is 6² (6 squared).

Following this pattern, the next number should be the cube of 7. Therefore, the next number is 7², which equals 49.