\ensuremath{\alpha}-nucleus single-folding cluster optical potentials based upon the \ensuremath{\alpha}-cluster model and an \ensuremath{\alpha}-\ensuremath{\alpha} interaction were generated for $m\ensuremath{\alpha}$-cluster structure targets $(m=3,$ 4, 6, 7, and 8). Angular distributions of the differential cross section of \ensuremath{\alpha} elastic scattering by ${}^{12}\mathrm{C},$ ${}^{16}\mathrm{O},$ and ${}^{28}\mathrm{Si}$ have been analyzed for various incident energies using the derived potentials. Also, single-folding optical model potentials were constructed using an \ensuremath{\alpha}-nucleon effective interaction to analyze the same data. Both models produced reasonable success in predicting scattering data, particularly at higher energies. The effect of uncertainties in the projectile and target nuclear densities on the results was investigated. The energy dependence of the calculated potentials is also discussed.