Bimagic 8x8 square

A bimagic square is a simple magic square, but it is also a simple magic square if you fill in the squares of the numbers (= number x number) in each cell. The 8x8 bimagic square is the smallest bimagic square.

		260	260	260	260	260	260	260	260				11180	11180	11180	11180	11180	11180	11180	11180
	260									260		11180									11180
260		56	34	8	57	18	47	9	31		11180		3136	1156	64	3249	324	2209	81	961
260		33	20	54	48	7	29	59	10		11180		1089	400	2916	2304	49	841	3481	100
260		26	43	13	23	64	38	4	49		11180		676	1849	169	529	4096	1444	16	2401
260		19	5	35	30	53	12	46	60		11180		361	25	1225	900	2809	144	2116	3600
260		15	25	63	2	41	24	50	40		11180		225	625	3969	4	1681	576	2500	1600
260		6	55	17	11	36	58	32	45		11180		36	3025	289	121	1296	3364	1024	2025
260		61	16	42	52	27	1	39	22		11180		3721	256	1764	2704	729	1	1521	484
260		44	62	28	37	14	51	21	3		11180		1936	3844	784	1369	196	2601	441	9

I have constructed a new 8x8 bimagic square by swapping 0 an 1 in the binary grids. I have constructed the inverse 8x8 bimagic square.

Original 8x8 bimagic square Inverse 8x8 bimagic square

*1x digit*								*1x digit*
0	0	0	1	0	1	1	1	1	1	1	0	1	0	0	0
1	0	0	0	1	1	1	0	0	1	1	1	0	0	0	1
0	1	1	1	0	0	0	1	1	0	0	0	1	1	1	0
1	1	1	0	1	0	0	0	0	0	0	1	0	1	1	1
1	1	1	0	1	0	0	0	0	0	0	1	0	1	1	1
0	1	1	1	0	0	0	1	1	0	0	0	1	1	1	0
1	0	0	0	1	1	1	0	0	1	1	1	0	0	0	1
0	0	0	1	0	1	1	1	1	1	1	0	1	0	0	0


*+ 2x digit*								*+ 2x digit*
0	1	0	1	1	0	1	0	1	0	1	0	0	1	0	1
1	0	1	0	0	1	0	1	0	1	0	1	1	0	1	0
1	0	1	0	0	1	0	1	0	1	0	1	1	0	1	0
0	1	0	1	1	0	1	0	1	0	1	0	0	1	0	1
0	1	0	1	1	0	1	0	1	0	1	0	0	1	0	1
1	0	1	0	0	1	0	1	0	1	0	1	1	0	1	0
1	0	1	0	0	1	0	1	0	1	0	1	1	0	1	0
0	1	0	1	1	0	1	0	1	0	1	0	0	1	0	1


*+ 4x digit*								*+ 4x digit*
0	1	0	1	1	0	1	0	1	0	1	0	0	1	0	1
1	1	0	0	0	0	1	1	0	0	1	1	1	1	0	0
1	1	0	0	0	0	1	1	0	0	1	1	1	1	0	0
1	0	1	0	0	1	0	1	0	1	0	1	1	0	1	0
0	1	0	1	1	0	1	0	1	0	1	0	0	1	0	1
0	0	1	1	1	1	0	0	1	1	0	0	0	0	1	1
0	0	1	1	1	1	0	0	1	1	0	0	0	0	1	1
1	0	1	0	0	1	0	1	0	1	0	1	1	0	1	0


*+ 8x digit*								*+ 8x digit*
1	1	1	0	1	0	0	0	0	0	0	1	0	1	1	1
1	1	1	0	1	0	0	0	0	0	0	1	0	1	1	1
0	0	0	1	0	1	1	1	1	1	1	0	1	0	0	0
1	1	1	0	1	0	0	0	0	0	0	1	0	1	1	1
0	0	0	1	0	1	1	1	1	1	1	0	1	0	0	0
1	1	1	0	1	0	0	0	0	0	0	1	0	1	1	1
0	0	0	1	0	1	1	1	1	1	1	0	1	0	0	0
0	0	0	1	0	1	1	1	1	1	1	0	1	0	0	0


*+ 16x digit*								*+ 16x digit*
0	1	1	0	0	1	1	0	1	0	0	1	1	0	0	1
1	0	0	1	1	0	0	1	0	1	1	0	0	1	1	0
0	1	1	0	0	1	1	0	1	0	0	1	1	0	0	1
0	1	1	0	0	1	1	0	1	0	0	1	1	0	0	1
1	0	0	1	1	0	0	1	0	1	1	0	0	1	1	0
1	0	0	1	1	0	0	1	0	1	1	0	0	1	1	0
0	1	1	0	0	1	1	0	1	0	0	1	1	0	0	1
1	0	0	1	1	0	0	1	0	1	1	0	0	1	1	0


*+ 32x digit + 1*								*+ 32x digit + 1*
0	0	1	0	1	0	1	1	1	1	0	1	0	1	0	0
0	1	0	0	1	1	0	1	1	0	1	1	0	0	1	0
1	0	1	1	0	0	1	0	0	1	0	0	1	1	0	1
1	1	0	1	0	1	0	0	0	0	1	0	1	0	1	1
1	1	0	1	0	1	0	0	0	0	1	0	1	0	1	1
1	0	1	1	0	0	1	0	0	1	0	0	1	1	0	1
0	1	0	0	1	1	0	1	1	0	1	1	0	0	1	0
0