We are given the series:
$51, 52, 60, 87, 151, \_\_\_\_, 492$

Let's analyze the differences between consecutive terms to identify a pattern:

1. $52 - 51 = 1$
2. $60 - 52 = 8$
3. $87 - 60 = 27$
4. $151 - 87 = 64$

The differences are:
$1, 8, 27, 64$

These differences are perfect cubes: $1 = 1^3, \quad 8 = 2^3, \quad 27 = 3^3, \quad 64 = 4^3$

Following this pattern, the next difference should be: $5^3 = 125$

Now, add this difference to the last number in the series: $151 + 125 = 276$

So, the missing value is 276.

Thus, the correct answer is:
(b) 276

Would you like further details or have any questions?

Here are 5 related questions to expand this concept:

1. What is the next number in the series after 492?
2. How would the series change if we used the squares of numbers instead of cubes?
3. What is the sum of the first five terms of the series?
4. Can we express this series as a mathematical function?
5. How do we identify patterns in more complex number sequences?

Tip: When analyzing a number sequence, look for patterns in differences, ratios, or powers to uncover hidden relationships.