So let me get this right

I believe the fastest way is as @TIG described …To align objects use inferencing
Infer and then click the Move tool on the bottom edge midpoint of a cube.
Then take that known point to another known point … the top edge midpoint of another cube.
That aligns their centers along one axis.
A second move, inferring to midpoints and constrained to the other axis, aligns their centers.

See: Inference Types — SketchUp Help … and then read Gully’s more eloquent description below.