Yes, indeed. All you need is two vertical and one horizontal cuts
One needs 6 movements to cut a cube into 27 pieces. Can you get this many pieces with fewer cuts? (Solution)
Can you cut a cube into 27 smaller cubes with fewer than 6 cuts? (The assumption being that one could not restack the pieces cut off previously but has - at all times - to preserve their combined cube shape.)
No, you can't because the center cube has 6 faces. You cannot obtain two of those with a single cut.