Using a quantum simulation approach, we investigate in the present work the spontaneous magnetic properties of two pairs of double-walled cylindrical nanotubes consisting of different spins. Our simulated magnetic and thermodynamic properties for each pair of them are precisely identical, exhibiting a fascinating property of the nature world and demonstrating the correctness of our simulation approach. The second pair of nanotubes are frustrated, two magnetic phases of distinct spin configurations appear in the low temperature region, but only the inner layer consisting of small spins is frustrated evidently, its magnetization is considerably suppressed in the high temperature phase. Moreover, the nanosystems exhibit typical Ising-like behavior due to the uniaxial anisotropy along the z-direction, and evident finite size effects as well. (C) 2016 Elsevier B.V. All rights reserved.