For an improved synthesis of the recently described expanded octamethoxycubane with a central C56 core, formally obtained by inserting buta-1,3-diynediyl moieties into all C(sp3)–C(sp3) bonds of octamethoxycubane, the preparation of the optically pure methyl ether of a differentially silyl-protected trispropargylic alcohol was required. The key step of the preparation involved a diastereoselective addition of a lithium acetylide to an optically active alkynyl ketone under Cram chelation control.