How can we label 3d cube?

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Yes, you can use text3d. The following code may give you some ideas:

v_opt = dict(fontsize="200%", fontfamily="palatino", fontstyle="italic", color="blue")
f_opt = dict(fontsize="200%", fontfamily="palatino", fontstyle="italic", color="black")

fig = cube(center=(0.5,0.5,0.5), size=1, color="lightgreen", frame_thickness=2, 
           frame_color="red", opacity=0.8)
fig += (text3d("A", (1.02,0,0), **v_opt) + text3d("B", (1.02,1.02,0), **v_opt)
        + text3d("C", (1.02,1.02,1.02), **v_opt) + text3d("D", (1.02,0,1.02), **v_opt)
        + text3d("E", (-0.02,0,0), **v_opt) + text3d("F", (-0.02,1.02,0), **v_opt)
        + text3d("G", (-0.02,1.02,1.02), **v_opt) + text3d("H", (-0.02,0,1.02), **v_opt))
fig += (text3d("front", (1.05,0.5,0.5),**f_opt) + text3d("back", (-0.05,0.5,0.5),**f_opt)
        + text3d("left", (0.5,-0.05,0.5),**f_opt) + text3d("right", (0.5,1.05,0.5),**f_opt)
        + text3d("up", (0.5,0.5,1.05),**f_opt) + text3d("down", (0.5,0.5,-0.05),**f_opt))
show(fig, frame=False)

This is the result, that you can also see in SageCell:

Two graphs are related:

• graphs.CubeGraph(3)
• graphs.GridGraph([2, 2, 2])

Their 2d plots and latexed forms have labels, but the 3d plots do not.

Cube graph

Define the cube graph

sage: C = graphs.CubeGraph(3)
sage: C
3-Cube: Graph on 8 vertices

Check its 2d plot, latex view, and 3d plot:

sage: C.plot()

sage: view(C)

sage: C.plot3d()

There is an option to get a different embedding:

sage: D = graphs.CubeGraph(3, embedding=2)
sage: D
3-Cube: Graph on 8 vertices

Check its 2d plot, latex view, and 3d plot:

sage: D.plot()

sage: view(D)

sage: D.plot3d()

Grid graph

The grid graph displays better:

sage: G = graphs.GridGraph([2, 2, 2])
sage: G
Grid Graph for [2, 2, 2]: Graph on 8 vertices

sage: G.plot()
Launched png viewer for Graphics object consisting of 21 graphics primitives

sage: view(G)

sage: G.plot3d()
Launched html viewer for Graphics3d Object