Summary: We consider \(D\)-dimensional Einstein gravity coupled to \((n-1)U(1)\) vector fields and \((n-2)\) dilatonic scalars. We find that for some appropriate exponential dilaton couplings of the field strengths, the equations of motion for the static charged ansatz can be reduced to a set of one-dimensional \(\mathrm{SL}(n,\mathbb R)\) Toda equations. This allows us to obtain a general class of explicit black holes with mass and \((n-1)\) independent charges. The near-horizon geometry in the extremal limit is \(\mathrm{AdS}_2 \times S^{D-2}\). The \(n = 2\) case gives the Reissner-Nordstrøm solution, and the \(n = 3\) example includes the Kaluza-Klein dyon. We study the global structure and the black hole thermodynamics and obtain the universal entropy product formula. We also discuss the characteristics of extremal multi-charge black holes that have positive, zero or negative binding energies.