The expression shown is a summation problem:

$\sum_{a=1}^{7} (a - 2)^3$

To solve this, we need to compute $(a - 2)^3$ for each integer value of $a$ from 1 to 7, then add the results.

Let's evaluate each term:

1. When $a = 1$: $(1 - 2)^3 = (-1)^3 = -1$
2. When $a = 2$: $(2 - 2)^3 = 0^3 = 0$
3. When $a = 3$: $(3 - 2)^3 = 1^3 = 1$
4. When $a = 4$: $(4 - 2)^3 = 2^3 = 8$
5. When $a = 5$: $(5 - 2)^3 = 3^3 = 27$
6. When $a = 6$: $(6 - 2)^3 = 4^3 = 64$
7. When $a = 7$: $(7 - 2)^3 = 5^3 = 125$

Now, summing these values:

$-1 + 0 + 1 + 8 + 27 + 64 + 125 = 224$

The result of the summation is:

$\sum_{a=1}^{7} (a - 2)^3 = 224$

Would you like more details or have any further questions?

Here are some related questions to expand your understanding:

1. What is the significance of using a summation in mathematical analysis?
2. How does changing the exponent affect the values in a summation?
3. What would the result be if the summation limits changed to different values?
4. How would the outcome differ if we summed $(a - 2)^2$ instead of $(a - 2)^3$?
5. How can summations be useful in calculating areas under curves or in other calculus applications?

Tip: Summation problems often benefit from organizing terms individually before performing arithmetic, which minimizes mistakes.