  The (2k+2)-dimensional Einstein-Yang-Mills equations for gauge group SO(2k)
(or SU(2) for k=2 and SU(3) for k=3) are shown to admit a family of
spherically-symmetric magnetic monopole solutions, for both zero and non-zero
cosmological constant Lambda, characterized by a mass m and a magnetic-type
charge. The k=1 case is the Reissner-Nordstrom black hole. The k=2 case yields
a family of self-gravitating Yang monopoles. The asymptotic spacetime is
Minkowski for Lambda=0 and anti-de Sitter for Lambda<0, but the total energy is
infinite for k>1. In all cases, there is an event horizon when m>m_c, for some
critical mass $m_c$, which is negative for k>1. The horizon is degenerate when
m=m_c, and the near-horizon solution is then an adS_2 x S^{2k} vacuum.
