10x10 and 11x11 magic squares of cubes.
10x10 and 11x11 magic squares of 4th powers.
10x10 and 11x11 magic squares of 5th powers.
See also the Magic squares of cubes general page

In October 2006, some days after the first known 9x9 magic square of cubes, I was pleased to construct the first known 10x10 magic square of cubes:

• it uses the first 100 cubes, from 1³ to 100³
• 1³, 2³, 3³, and 4³ are placed in the first row
   

October 2006: first known 10x10 magic square of cubes,
by Christian Boyer. S3 = 2,550,250

143	933	43	13	23	33	943	303	93	963
863	543	53	903	803	263	353	173	653	563
193	133	873	773	233	153	593	913	313	753
213	473	693	273	443	993	463	643	673	723
1003	453	343	283	603	83	533	813	793	203
413	103	893	743	513	613	163	823	683	523
403	783	713	73	383	223	853	183	953	483
333	973	493	923	293	363	573	623	253	583
763	113	63	433	983	883	323	373	633	423
663	123	703	393	833	843	733	503	243	553

And in November 2006, I constructed the first known 11x11 magic square of cubes:

• it uses the first 121 cubes, from 1³ to 121³
• all 11 rows remain magic when the entries are not cubed. S1=671.
   

November 2006: first known 11x11 magic square of cubes,
by Christian Boyer. S3 = 4,952,651.

363	843	333	113	633	1003	923	1193	23	653	663
513	343	313	763	243	883	373	143	1153	1053	963
743	573	1063	353	83	1033	323	623	583	203	1163
863	783	223	873	183	103	703	1213	973	393	433
1093	793	643	1133	493	553	253	673	123	33	953
53	213	503	563	693	13	933	723	993	1073	983
593	153	753	1023	713	413	1183	173	193	1013	533
423	1123	853	733	1103	43	943	543	403	133	443
813	283	913	273	1113	1083	603	63	823	613	163
1173	73	303	263	1043	833	463	683	903	773	233
293	1203	1143	893	383	483	523	473	93	803	453

Open problems:

• 10x10 and 11x11 magic squares of 4th powers are unknown.
• 10x10 and 11x11 magic squares of 5th powers are unknown.

March 2018, Nicolas Rouanet, France, constructed this 10x10 (and also a 12x12) nearly-magic square of consecutive 4th powers, from 1^4 to 100^4:

March 2018: 10x10 semi-magic square of 4th powers,
with one magic diagonal, by Nicolas Rouanet, S4 = 205,033,333.

444	374	184	524	824	874	254	854	734	544
24	774	744	954	74	144	264	344	834	554
354	124	634	174	134	364	924	484	604	994
14	594	904	864	284	314	104	574	884	274
814	1004	534	224	654	464	514	644	474	424
684	624	294	794	454	764	584	394	154	944
894	194	404	164	724	934	334	704	564	414
204	64	914	674	714	304	974	114	324	244
694	804	44	54	964	94	664	234	784	214
844	34	614	384	84	754	494	984	434	504

Nicolas Rouanet remarked, using modulo 5 reasoning, that an 11x11 magic (or semi-magic) square is impossible using consecutive 4th powers, from 1^4 to 121^4.

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