We study experimentally the dependence of dynamic nuclear spin polarization on the power of non-resonant optical excitation in two types of individual neutral semiconductor quantum dots: In-GaAs/GaAs and GaAs/AlGaAs. We show that the mechanism of nuclear spin pumping via second order recombination of optically forbidden (" dark ") exciton states recently reported in InP/GaInP quantum dots [Phys. Rev. B 83, 125318 (2011)] is relevant for material systems considered in this work. In the InGaAs/GaAs dots this nuclear spin polarization mechanism is particularly pronounced , resulting in Overhauser shifts up to ∼80 µeV achieved at optical excitation power ∼1000 times smaller than the power required to saturate ground state excitons. The Overhauser shifts observed at low-power optical pumping in the interface GaAs/AlGaAs dots are generally found to be smaller (up to ∼40 µeV). Furthermore in GaAs/AlGaAs we observe dot-to-dot variation and even sign reversal of the Overhauser shift which is attributed to dark-bright exciton mixing originating from electron-hole exchange interaction in dots with reduced symmetry. Nuclear spin polarization degrees reported in this work under ultra-low power optical pumping are comparable to those achieved by techniques such as resonant optical pumping or above-gap pumping with high power circularly polarized light. Dynamic nuclear polarization via second-order recombination of " dark " excitons may become a useful tool in single quantum dot applications, where manipulation of the nuclear spin environment or electron spin is required.