Deriving the Sum of Cubes Formula - Through Volume

GeoGebra Commands & Parameters

1. Polygon(A, B, C, D) → poly1, a, b, c, d
2. Polygon(D, E, F, A) → poly2, d_1, e, f, a_1
3. Polygon(C, G, E, D) → poly3, c_1, g, e_1, d_2
4. Segment(F, H) → h
5. Segment(H, G) → i
6. Segment(H, B) → j
7. Point(c) → I
8. Point(b) → K
9. Polygon(C, I, J, K) → poly4, c_2, i_1, j_1, k
10. Point(c_1) → M
11. Polygon(I, L, M, C) → poly5, i_2, l, m, c_3
12. Polygon(L, N, J, I) → poly6, l_1, n_{18}, j_2, i_3
13. Point(g) → O
14. Line(I, O) → p
15. Line(J, N) → q
16. Point(h) → Q
17. Polygon(N, P, Q, R) → poly7, n_1, p_1, q_1, r
18. Point(e) → S
19. Polygon(R, S, F, Q) → poly8, r_1, s, f_1, q_2
20. Point(f) → T
21. Polygon(P, T, U, N) → poly9, p_2, t, u, n_2
22. Polygon(U, S, R, N) → poly10, u_1, s_1, r_2, n_3
23. Polygon(T, F, S, U) → poly11, t_1, f_2, s_2, u_2
24. Segment(N, V) → b_1
25. Segment(V, K) → g_1
26. Segment(V, M) → h_1
27. Segment(Q, R) → k_1
28. Segment(Q, P) → m_1
29. Polygon(L, O, G, M) → poly12, l_2, o, g_2, m_2
30. Polygon(O, R, N, L) → poly13, o_1, r_3, n_4, l_3
31. Polygon(N, L, M, V) → poly14, n_5, l_4, m_3, v
32. Segment(R, W) → a_2
33. Segment(W, G) → b_2
34. Segment(W, V) → e_2
35. Point(j) → Z
36. Polygon(V, Z, B, K) → poly15, v_1, z_1, b_3, k_2
37. Point(a) → A_1
38. Polygon(J, A_1, B, K) → poly16, j_3, a_3, b_4, k_3
39. Polygon(A_1, P, N, J) → poly17, a_4, p_3, n_6, j_4
40. Polygon(K, V, N, J) → poly18, k_4, v_2, n_7, j_5
41. Point(d) → B_1
42. Point(d_1) → C_1
43. Polygon(U, B_1, D, C_1) → poly19, u_3, b_5, d_3, c_4
44. Polygon(D, C_1, L, I) → poly20, d_4, c_5, l_5, i_4
45. Polygon(I, J, B_1, D) → poly21, i_5, j_6, b_6, d_5
46. Polygon(C_1, E, O, L) → poly22, c_6, e_3, o_2, l_6
47. Polygon(C_1, E, S, U) → poly23, c_7, e_4, s_3, u_4
48. Polygon(U, N, L, C_1) → poly24, u_5, n_8, l_7, c_8
49. Polygon(B_1, A, A_1, J) → poly25, b_7, a_5, a_6, j_7
50. Polygon(A, B_1, U, T) → poly26, a_7, b_8, u_6, t_2
51. Polygon(U, N, J, B_1) → poly27, u_7, n_9, j_8, b_9
52. Segment(B, C) → h_2
53. Segment(C, G) → f_3
54. Segment(G, H) → g_3
55. Segment(H, B) → h_3
56. Segment(B, A) → q_3
57. Segment(C, D) → t_3
58. Segment(D, E) → f_4
59. Segment(E, G) → g_4
60. Segment(A, D) → h_4
61. Segment(A, F) → m_4
62. Segment(F, E) → p_4
63. Segment(K, B_1) → q_4
64. Segment(A_1, I) → r_4
65. Segment(I, O) → s_4
66. Segment(M, C_1) → t_4
67. Segment(B_1, S) → e_5
68. Segment(T, C_1) → f_5
69. Segment(P, L) → g_5
70. Segment(A_1, Q) → h_5
71. Segment(J, R) → k_5
72. Segment(W, S) → m_5
73. Segment(V, U) → p_5
74. Segment(Q, O) → q_5
75. Segment(Z, M) → r_5
76. Segment(Z, T) → s_5
77. Polygon(K, C, M, V) → poly28, k_6, c_9, m_6, v_3
78. Polygon(K, V, N, J) → poly29, k_7, v_4, n_{10}, j_9
79. Polygon(V, M, G, W) → poly30, v_5, m_7, g_6, w_3
80. Polygon(J, I, L, N) → poly31, j_{10}, i_6, l_8, n_{11}
81. Polygon(Z, V, N, P) → poly32, z_2, v_6, n_{12}, p_6
82. Polygon(V, W, R, N) → poly33, v_7, w_4, r_6, n_{13}
83. Polygon(P, N, R, Q) → poly34, p_7, n_{14}, r_7, q_6
84. Polygon(Z, V, W, H) → poly35, z_3, v_8, w_5, h_6
85. Polygon(N, L, O, R) → poly36, n_{15}, l_9, o_6, r_8
86. Polygon(A_1, J, N, P) → poly37, a_8, j_{11}, n_{16}, p_8
87. Polygon(P, N, R, Q) → poly38, p_9, n_{17}, r_9, q_7
88. Polygon(P, Q, F, T) → poly39, p_{10}, q_8, f_6, t_6
89. Segment(D_1, E_1) → e_6
90. Segment(R, S) → f_7