Cubes in Cubes
The following pictures show n unit cubes packed inside the smallest known cube (of side s). For all other values of n < 512, the trivial packing is the best known.

9-10.
           11.
           12.
           13.
s = 2 + 1/√2 = 2.70710+
Found by Erich Friedman
in 1998. 		s = 2.88171+
Found by Stian Sønderland
in October 2026. 		s = 2.93151+
Found by Yohei Nakajima
in October 2026. 		s = 2.95614+
Found by Ryan Hayes in
October 2026.

14.
           28.
           29.-33.
           34.
s = 2 + 7√2/10 = 2.98994+
Found by Erich Friedman
in 1998. 		s = 3.66600+
Found by Hirotaka Nakano
in October 2026. 		s = 3 + 1/√2 = 3.70710+
Found by Erich Friedman
in 1998. 		s = 3.99899+
Found by Mohsen Karimi
in November 2026.
65.-68.
           69.-76.
           126.-130.
           131.-143.
s = 4.67553+
Trivial. 		s = 4 + 1/√2 = 4.70710+
Found by Mohsen Karimi
in November 2026. 		s = 5.62132+
Trivial. 		s = 5 + 1/√2 = 5.70710+
Found by Mohsen Karimi
in November 2026.
144.-145.
           217.-222.
           231.-239.
           240.
s = 5.93383+
Trivial. 		s = 6.59861+
Trivial. 		s = 6 + 1/√2 = 6.70710+
Found by Mohsen Karimi
in November 2026. 		s = 4+2√2 = 6.82842+
Trivial.
241.-246.
           344.-350.
           351.-357.
           358.-364.
s = 6.92669+
Trivial. 		s = 53/7 = 7.57142+
Trivial. 		s = 7.70079+
Trivial. 		s = 7 + 1/√2 = 7.70710+
Trivial.
365.-371.
           372.-378.
           379.-385.
           386.-390.
s = 13/2 + √7/2 = 7.82287+
Trivial. 		s = 7.84666+
Trivial. 		s = 7.94577+
Trivial. 		s = 7.99899+
Found by Mohsen Karimi
in November 2026.
561.-568.
           569.-584.
           793.-801.
           802.-819.
s = 8.94407+
Trivial. 		s = 8.99899+
Found by Mohsen Karimi
in November 2026. 		s = 9.94974+
Trivial. 		s = 9.99898+
Found by Mohsen Karimi
in November 2026.