The unit digit of a number ending with 6 will always be 6 itself when it is cubed. This can be explained using the concept of cyclicity of numbers.

Cyclicity refers to the pattern in which the unit digit of a number repeats itself when the number is raised to different powers. For example, if we consider the unit digits of the numbers 6, 6^2, 6^3, 6^4, and so on, we can observe the following pattern:

6^1 = 6
6^2 = 36
6^3 = 216
6^4 = 1296
6^5 = 7776
6^6 = 46656

From the above pattern, we can see that the unit digit of 6^1, 6^2, 6^3, and so on is always 6. Therefore, when a number ending with 6 is cubed, the unit digit will also be 6.

To further understand this concept, we can also use the concept of remainders when dividing numbers by 10. When a number is divided by 10, the remainder gives us the unit digit of the number. For example, when we divide 16 by 10, the remainder is 6.

Now, let's consider the cube of 16. When we calculate 16^3, we can write it as (10 + 6)^3. Expanding this expression using the binomial theorem, we get:

16^3 = (10 + 6)^3 = 10^3 + 3 * 10^2 * 6 + 3 * 10 * 6^2 + 6^3

The first three terms in the expansion, 10^3, 3 * 10^2 * 6, and 3 * 10 * 6^2, will all have 0 as their unit digit because they are multiples of 10. The last term, 6^3, will have a unit digit of 6.

Therefore, the unit digit of the cube of a number ending with 6 will always be 6. Hence, the correct answer is option 'B'.