please use proper grouping symbols ...
(y^3 - 64)/(y - 4)
y^3 - 64 = y^3 - 4^3, is the difference between two cubes ... which does factor.
fyi ... the factoring pattern is a^3 - b^3 = (a - b)(a^2 + ab + b^2)
also, the sum of two cubes is also factorable ...
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
place these two algebra factoring facts into your algebra "toolbox" ... you will see them again.