\[{y}^{3}-8\]
1
Rewrite it in the form a3−b3{a}^{3}-{b}^{3}, where a=ya=y and b=2b=2.
y3−23{y}^{3}-{2}^{3}

2
Use Difference of Cubes: a3−b3=(a−b)(a2+ab+b2){a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2}).
(y−2)(y2+(y)(2)+22)(y-2)({y}^{2}+(y)(2)+{2}^{2})

3
Simplify  22{2}^{2}  to  44.
(y−2)(y2+y×2+4)(y-2)({y}^{2}+y\times 2+4)

4
Regroup terms.
(y−2)(y2+2y+4)(y-2)({y}^{2}+2y+4)

Done
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