Expand $(y + 8)^3$ using the binomial formula $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$:

$(y + 8)^3 = y^3 + 3(y^2)(8) + 3(y)(64) + 512$

$= y^3 + 24y^2 + 192y + 512$