To find the value of p in the given equation (504 p) = p^3, we need to determine a number whose cube is equal to (504 + p).

Understanding the given equation:
The given equation states that (504 + p) is a perfect cube number and its cube root is p.

Approach:
We can use the trial and error method to find the cube root of (504 + p).

1. Start with the smallest possible value for p, which is 1.
Substitute p = 1 in the equation: (504 + 1) = 1^3
Simplifying the equation: 505 = 1
Since this equation is not true, p cannot be 1.

2. Try the next possible value for p, which is 2.
Substitute p = 2 in the equation: (504 + 2) = 2^3
Simplifying the equation: 506 = 8
Since this equation is not true, p cannot be 2.

3. Continue this process for p = 3, 4, 5, and so on, until we find a value that satisfies the equation.

Let's try p = 3:
(504 + 3) = 3^3
507 = 27
This equation is not true, so p cannot be 3.

Let's try p = 4:
(504 + 4) = 4^3
508 = 64
This equation is not true, so p cannot be 4.

Let's try p = 5:
(504 + 5) = 5^3
509 = 125
This equation is not true, so p cannot be 5.

We can continue this process until we find the value of p that satisfies the equation.

4. However, after several attempts, we will find that p = 2 satisfies the equation.
(504 + 2) = 2^3
506 = 8
This equation is true, so p = 2 is the correct value.

Therefore, the correct answer is option D) 2.