What number should replace question Mark(?1) in the series given below.

55, 47, 74, 10, 135, 81, 262?

The correct option is -250.

To find the missing number in the series, let us analyze the pattern of differences between consecutive terms:
55, 47, 74, 10, 135, -81 (printed as 81 in the question due to a sign typo), 262, ?

The sequence progresses by alternately subtracting and adding the cubes of consecutive integers starting from 2:

$1\text{st term}=55$

$2\text{nd term}=55-2^3=55-8=47$

$3\text{rd term}=47+3^3=47+27=74$

$4\text{th term}=74-4^3=74-64=10$

$5\text{th term}=10+5^3=10+125=135$

$6\text{th term}=135-6^3=135-216=-81$
(Note: The question contains a minor typo where -81 is written as 81.)

$7\text{th term}=-81+7^3=-81+343=262$

Following this established logical mathematical pattern, the next term is obtained by subtracting the cube of 8:

$8\text{th term}=262-8^3=262-512=-250$

Therefore, the number that should replace the question mark is -250.