According to the laws of thermodynamics, materials normally exhibit contraction or expansion along the directions of the applied pressure or tension. Here, we show that a man-made cocrystal of a metallofullerene and highly energetic cubane, with strained sp3 bonding, may exhibit an anomalous negative volume compressibility. In this cocrystal, the freely rotating fullerene Sc3N@C80 acts as a structural building block while static cubane molecules fill the lattice interstitial sites. Under high pressure, Sc3N@C80 keeps stable and preserves the crystalline framework of the materials, while the cubane undergoes a progressive configurational transformation above 6.5 GPa, probably promoted by charge transfer from fullerene to cubane. A further configurational change of the cubane into a low-density configuration at higher pressure results in an anomalous pressure-driven lattice expansion of the cocrystal (∼1.8% volume expansion). Such unusual negative compressibility has previously only been predicted by theory and suggested to appear in mechanical metamaterials.