The formation, growth and detachment of gas bubbles on electrodes are omnipresent in electrolysis and other gas-producing chemical processes. To better understand their role in the mass transfer efficiency, we perform experiments involving successive bubble nucleations from a predefined nucleation site which consists of a superhydrophobic pit on top of a micromachined pillar. The experiments on bubble nucleation at these spots permit the comparison of mass transfer phenomena connected to electrolytically generated H2 bubbles with the better-understood evolution of CO2 bubbles in pressure-controlled supersaturated solutions. In both these cases, bubbles grow in a diffusion-dominated regime. For CO2 bubbles, it is found that the growth rate coefficient of subsequent bubbles always decreases due to the effect of gas depletion. In contrast, during constant current electrolysis the bubble growth rates are affected by the evolution of a boundary layer of dissolved H2 gas near the flat electrode which competes with gas depletion. This competition results in three distinct regimes. Initially, the bubble growth slows down with each new bubble in the succession due to the dominant depletion of the newly-formed concentration boundary layer. In later stages, the growth rate increases due to a local increase of gas supersaturation caused by the continuous gas production and finally levels off to an approximate steady growth rate. The gas transport efficiency associated with the electrolytic bubble succession follows a similar trend in time. Finally, for both H2 and CO2 bubbles, detachment mostly occurs at smaller radii than theory predicts and at a surprisingly wide spread of sizes. A number of explanations are proposed, but the ultimate origin of the spreading of the results remains elusive.