The many-electron response of a small-diameter conducting carbon nanotube, to the sudden creation of a 1s core state, is studied using density functional theory with different Gaussian basis sets and the generalized gradient approximation for exchange and correlation. Cluster computations are performed on carbon atoms located at a finite-size cylindrical network that is terminated by hydrogen atoms. Core-hole creation is simulated by replacing the 1s electron pair, localized at a central site of the structure, with effective pseudo-potentials for both neutral and ionized atomic carbon. The same approach is used to describe a neutral and core-ionized C-60 fullerene molecule. The overlaps between the excited states of the ionized systems and the ground states of the neutral systems are combined in a Fermi's golden rule treatment yielding the shake-up spectra from the two clusters. The numerical response for the fullerene molecule is found in good agreement with the measured X-ray photoelectron spectrum from thick C-60 films, including the low energy satellites at excitation energies below 4 eV, within a peak position error of 0.3 eV. The nanotube spectrum reveals features in common with X-ray photoelectron data from Bucky balls and Bucky papers. (C) 2013 Elsevier B.V. All rights reserved.