We investigate the dynamic nuclear spin polarization in an n-GaAs lateral channel induced by electrical spin injection from a (Ga,Mn)As/n-GaAs spin Esaki diode. Signatures of nuclear spin polarization are studied in both three-terminal and non-local voltage signals, where a strong electron spin depolarization feature is observed close to zero magnetic field. This is due to the large nuclear field induced in the channel through hyperfine interaction between injected electron spins and localized nuclear spins. We study the time evolution of the dynamic nuclear spin polarization and evaluate polarization and relaxation times of nuclear spins in the channel. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767339]