Use a 4x4 panmagic square to construct a Franklin panmagic 16x16x16 cube.

 

 

Take 1x number from first grid [level 1]

1	8	13	12	1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7	14	11	2	7
1	8	13	12	1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7	14	11	2	7
1	8	13	12	1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7	14	11	2	7
1	8	13	12	1	8	13	12	1	8	13	12	1	8	13	12
15	10	3	6	15	10	3	6	15	10	3	6	15	10	3	6
4	5	16	9	4	5	16	9	4	5	16	9	4	5	16	9
14	11	2	7	14	11	2	7	14	11	2	7	14	11	2	7

 

 

+ 16x number from second grid [level 1]

0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1
0	3	3	0	3	0	0	3	1	2	2	1	2	1	1	2
3	0	0	3	0	3	3	0	2	1	1	2	1	2	2	1

 

 

+ 64x number from third grid [level 1]

0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3
3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0
3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0
0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3
3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0
0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3
0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3
3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0
1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2
2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1
2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1
1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2
2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1
1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2
1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2
2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1

 

 

+ 256x number from fourth grid [level 1]

1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1
1	1	16	16	1	1	16	16	1	1	16	16	1	1	16	16
16	16	1	1	16	16	1	1	16	16	1	1	16	16	1	1

 

 

= Franklin panmagic 16x16x16 cube [level 1]

1	248	3901	4044	49	200	3853	4092	17	232	3885	4060	33	216	3869	4076
4095	3850	195	54	4047	3898	243	6	4079	3866	211	38	4063	3882	227	22
196	53	4096	3849	244	5	4048	3897	212	37	4080	3865	228	21	4064	3881
3902	4043	2	247	3854	4091	50	199	3886	4059	18	231	3870	4075	34	215
193	56	4093	3852	241	8	4045	3900	209	40	4077	3868	225	24	4061	3884
3903	4042	3	246	3855	4090	51	198	3887	4058	19	230	3871	4074	35	214
4	245	3904	4041	52	197	3856	4089	20	229	3888	4057	36	213	3872	4073
4094	3851	194	55	4046	3899	242	7	4078	3867	210	39	4062	3883	226	23
65	184	3965	3980	113	136	3917	4028	81	168	3949	3996	97	152	3933	4012
4031	3914	131	118	3983	3962	179	70	4015	3930	147	102	3999	3946	163	86
132	117	4032	3913	180	69	3984	3961	148	101	4016	3929	164	85	4000	3945
3966	3979	66	183	3918	4027	114	135	3950	3995	82	167	3934	4011	98	151
129	120	4029	3916	177	72	3981	3964	145	104	4013	3932	161	88	3997	3948
3967	3978	67	182	3919	4026	115	134	3951	3994	83	166	3935	4010	99	150
68	181	3968	3977	116	133	3920	4025	84	165	3952	3993	100	149	3936	4009
4030	3915	130	119	3982	3963	178	71	4014	3931	146	103	3998	3947	162	87

 

 

Each level consists of 16 proportional panmagic 4x4 squares. The cube is in each level panmagic and 2x2 compact and each 1/4 row/column/diagonal gives 1/4 of the magic sum. The cube is pandiagonal and pantriagonal magic through the levels and each 1/4 pillar gives 1/4 of the magic sum and each 1/2 tridiagonal gives 1/2 of the magic sum.

 

See all grids and all levels of the 16x16x16 magic cube in the downloads below.

 

With method composite 1 you use a magic square to construct a magic cube. See on this website the construction of:

3x3x3 (simple),  4x4x4 (most perfect), 5x5x5 (pantriagonal), 7x7x7 (pantriagonal),

9x9x9 (pandiagonal & compact), 12x12x12 (diagonal), 12x12x12 (pantriagonal),

15x15x15 (pandiagonal & compact), 16x16x16 (Nasik)a, 16x16x16 (Nasik)b,

20x20x20 (diagonal), 20x20x20 (pantriagonal), 24x24x24 (diagonal), 24x24x24

(pantriagonal), 28x28x28 (diagonal), 28x28x28 (pantriagonal)