glucylinder in cube

I am trying to get see through the hole on the cube by glucylinder. The problem is GL_QUADS cover the hole by glucylinder(you see circle, but you cant see through it). it works with GL_LINE_LOOP, but I really want to use with GL_QUADS bec it looks better. Any suggestions? Thanks in advance!!

public override void glDraw()
{

glClearColor(1.0f, 1.0f, 1.0f, 1.0f);//background color
glColor3f(0.0f,0.0f,0.0f);//black

glBegin(GL.GL_QUADS);//top
glVertex3f(1, 1, -1);
glVertex3f(-1, 1, -1);
glVertex3f(-1, 1, 1);
glVertex3f(1, 1, 1);
glEnd();

glBegin(GL.GL_QUADS);
glVertex3f(-1, -1, 1);//bottom
glVertex3f(1, -1, 1);
glVertex3f(1, -1, -1);
glVertex3f(-1, -1, -1);
glEnd();

glBegin(GL.GL_QUADS);
glVertex3f(1, 1, 1);//front
glVertex3f(-1, 1, 1);
glVertex3f(-1, -1, 1);
glVertex3f(1, -1, 1);
glEnd();

glBegin(GL.GL_QUADS);
glVertex3f(-1, 1, -1);//back
glVertex3f(1, 1,-1);
glVertex3f(1, -1, -1);
glVertex3f(-1, -1, -1);
glEnd();

glBegin(GL.GL_QUADS);
glVertex3f(-1,1,1); //left
glVertex3f(-1,1,-1);
glVertex3f(-1,-1,-1);
glVertex3f(-1,-1,1);
glEnd();

glBegin(GL.GL_QUADS);
glVertex3f(1,1,-1);//right
glVertex3f(1,1,1);
glVertex3f(1,-1, 1);
glVertex3f(1,-1,-1);
glEnd();

glPushMatrix();
glColor3f(1.0f,0.0f,1.0f);//pink

gluQuadricDrawStyle(cyl,GL.GL_FILL);
gluQuadricNormals(cyl, GL.GL_SMOOTH);
gluCylinder(cyl, rad, rad2, height, 20, 100);
glPopMatrix();

}

What you want to do is not clear to me.
Can you be more precise / have better english / put some handrawn pictures ?

Moreover, it looks more like a beginner problem (gluCylinder and the like). Try to draw your own cylinder, it will be more flexible. Believe me, it is not very difficult.

Search the keyword “CSG” in this forum, and you should read a trick using stencil buffer.