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In this article, we construct non-compact complete Einstein metrics on twoinfinite series of manifolds. The first series of manifolds are vector bundleswith $\mathbb{S}^{4m+3}$ as principal orbit and $\mathbb{HP}^{m}$ as singularorbit. The second series of manifolds are $\mathbb{R}^{4m+4}$ with the sameprincipal orbit. For each case, a continuous 1-parameter family of completeRicci-flat metrics and a continuous 2-parameter family of complete negativeEinstein metrics are constructed. In particular, $\mathrm{Spin}(7)$ metrics$\mathbb{A}_8$ and $\mathbb{B}_8$ discovered by Cveti\v{c} et al. in 2004 arerecovered in the Ricci-flat family. A Ricci flat metric with conicalsingularity is also constructed on $\mathbb{R}^{4m+4}$. Asymptotic limits ofall Einstein metrics constructed are studied. Most of the Ricci-flat metricsare asymptotically locally conical (ALC). Asymptotically conical (AC) metricsare found on the boundary of the Ricci-flat family. All the negative Einsteinmetrics constructed are asymptotically hyperbolic (AH).

Einstein metrics of cohomogeneity one with $S^{4m+3}$ as principal orbit