27a3+64 is of the type x3+y3=(x+y)(x2-xy+y2).
So x3=27a3, making x=3a; and y3=64, making y=4.
27a3+64=(3a+4)(9a2-12a+16).
It factorises further but the factors are complex (not real):
x2-xy+y2=(x-½y+½iy√3)(x-½y-½iy√3) where i=√-1.
9a2-12a+16=(3a-2+2i√3)(3a-2-2i√3)=9a2-12a+4+12=9a2-12a+16.