To find the missing number in the sequence 4, 16, ____, 256, 1,024, we can observe the pattern of the numbers:
- 4 is \( 4^1 \) or \( 2^2 \)
- 16 is \( 4^2 \) or \( 2^4 \)
- 256 is \( 4^4 \) or \( 2^8 \)
- 1,024 is \( 4^5 \) or \( 2^{10} \)
The powers of 4 used are \( 1, 2, 3, 4, 5 \).
Thus, the missing number corresponds to \( 4^3 \) which is:
\[ 4^3 = 64 \]
Therefore, the missing number is 64.