Unwanted lines with GL_POLYGON_SMOOTH

Why do the edges of the cubes give these effects when i do

glEnable(GL_POLYGON_SMOOTH)
glHint(GL_POLYGON_SMOOTH_HINT, GL_NICEST)

Is there a way to get rid of them?

Because you do not have the right blend mode set.

You need:

glEnable(GL_BLEND)
glBlendFunc(GL_SRC_ALPHA_SATURATE,GL_ONE)

Also I am not sure but maybe you need to sort polygons by Z?