Currently I am drawing a cube for a game that I am making and the cube draw method is below. My question is, what is the best way to draw a cube and to be able to easily find the face that the cursor is over? My draw method works just fine, but I am getting ready to start to add picking (this will be used to mold the cubes into other shaps), and would like to know the best way to find a face of the cube.

public void  Draw() {   
    // center point posX, posY, posZ
    float radius = size / 2;

    //top
    glPushMatrix();
    glBegin(GL_QUADS);
        {
            glColor3f(1.0f,0.0f,0.0f); // red
            glVertex3f(posX + radius, posY + radius, posZ - radius);
            glVertex3f(posX - radius, posY + radius, posZ - radius);
            glVertex3f(posX - radius, posY + radius, posZ + radius);
            glVertex3f(posX + radius, posY + radius, posZ + radius);
        }
    glEnd();
    glPopMatrix();

    //bottom
    glPushMatrix();
    glBegin(GL_QUADS);
        {
            glColor3f(1.0f,1.0f,0.0f); // ?? color
            glVertex3f(posX + radius, posY - radius, posZ + radius);
            glVertex3f(posX - radius, posY - radius, posZ + radius);
            glVertex3f(posX - radius, posY - radius, posZ - radius);
            glVertex3f(posX + radius, posY - radius, posZ - radius);
        }
    glEnd();
    glPopMatrix();

    //right side
    glPushMatrix();
    glBegin(GL_QUADS);
        {
            glColor3f(1.0f,0.0f,1.0f); // ?? color
            glVertex3f(posX + radius, posY + radius, posZ + radius);
            glVertex3f(posX + radius, posY - radius, posZ + radius);
            glVertex3f(posX + radius, posY - radius, posZ - radius);
            glVertex3f(posX + radius, posY + radius, posZ - radius);
        }
    glEnd();
    glPopMatrix();

    //left side
    glPushMatrix();
    glBegin(GL_QUADS);
        {
            glColor3f(0.0f,1.0f,1.0f); // ?? color
            glVertex3f(posX - radius, posY + radius, posZ - radius);
            glVertex3f(posX - radius, posY - radius, posZ - radius);
            glVertex3f(posX - radius, posY - radius, posZ + radius);
            glVertex3f(posX - radius, posY + radius, posZ + radius);
        }
    glEnd();
    glPopMatrix();

    //front side 
    glPushMatrix();
    glBegin(GL_QUADS);
        {
            glColor3f(0.0f,0.0f,1.0f); // blue 
            glVertex3f(posX + radius, posY + radius, posZ + radius);
            glVertex3f(posX - radius, posY + radius, posZ + radius);
            glVertex3f(posX - radius, posY - radius, posZ + radius);
            glVertex3f(posX + radius, posY - radius, posZ + radius);
        }
    glEnd();
    glPopMatrix();

    //back side
    glPushMatrix();
    glBegin(GL_QUADS);
        {
            glColor3f(0.0f,1.0f,0.0f); // green
            glVertex3f(posX + radius, posY - radius, posZ - radius);
            glVertex3f(posX - radius, posY - radius, posZ - radius);
            glVertex3f(posX - radius, posY + radius, posZ - radius);
            glVertex3f(posX + radius, posY + radius, posZ - radius);
        }
    glEnd();
    glPopMatrix();
}