Answer
$a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}$)
Work Step by Step
Consider the area of the three rectangular blocks individually and then add them together.
1) the area of the orange block is
$a * a * (a-b)$
2) the area of the blue block is
$a * (a-b) * b$
3) the area of the yellow block is
$(a+b) * b * b$
The total of them would be
$a * a * (a-b) + a * (a-b) * b + (a+b) * b * b$
= $a^{3}$ - $a^{2}$b + a$b^{2}$ + $b^{3}$ + $a^{2}$b - a$b^{2}$
Taking the common factor out from the two groups of three, it becomes
= $a ( a^{2} - ab + b^{2} ) + b ( b^{2} + a^{2} - ab)$
= $(a + b) (a^{2}-ab+b^{2})$
Therefore, $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2}$).
