Swaziland

[TimberWolf]

Yea, muppets. Lucky they weren't asked for the smallest integer cube that's the sum of four consecutive integer cubes.

Second smallest

[OwlHoot]

Yea, muppets. Lucky they weren't asked for the smallest integer cube that's the sum of four consecutive integer cubes.

Whoops - four consecutive *positive* integer cubes.

Otherwise there's a trivial solution -1^3 + 0^3 + 1^3 + 2^3 = 2^3