First centres

Big cubes are solved by reduction, as the 4x4: build the centres, pair each edge's pieces, then solve the cube as a 3x3 with outer turns. The last centres and the last edges are where algorithms help; the rest is intuitive.

Odd cubes (5x5, 7x7) have a fixed middle edge piece, so their last edges can show a flipped edge parity that pairing fixes; even cubes (6x6) also have the 4x4's parities, from swapped inner slices.