In this paper various deterministic and statistical models, based on new quantized theories proposed by the author, are presented for estimating the strength of a real, and thus defective, space elevator cable. The cable, ~100 000 km in length, is composed of carbon nanotubes, ~100 nm long: thus, its design involves nanomechanics and megamechanics. The predicted strengths are extensively compared with the experimental and atomistic simulation results for carbon nanotubes available in the literature. All these approaches unequivocally suggest that the megacable strength will be reduced by a factor at least of ~70% with respect to the theoretical nanotube strength, today (erroneously) assumed in the cable design. The reason is the unavoidable presence of defects in so huge a cable. Preliminary in-silicon tensile experiments confirm the same finding. The deduced strength reduction is sufficient to place in doubt the effective realization of the space elevator, that if built as designed today will certainly break (in the author's opinion). The mechanics of the cable is also revised and possible damage sources discussed.