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Knowledge of glacier ice volumes is crucial for constraining future sea level rise, evaluating freshwater resources, and assessing impacts on societies, from regional to global. Yet, significant uncertainties persist in both regional estimates of total glacier ice volume and in distributed ice thickness for individual glaciers. Here, we present the results from IceBoost v2.0, a machine learning system able to model the ice thickness of individual glaciers, trained on 7 million ice thickness measurements and informed by physical and geometrical predictors. Globally, we find a total glacier volume of (149 ± 38) × 103 km3 and sea level equivalent of 323 ± 91 mm, both well within existing estimates. We examine major glaciated regions and compare the results with other models. Confidence in our solution is highest at higher latitudes, where abundant training data adequately sample the feature space. Over steep and mountainous terrain, small glaciers, and under-represented lower-latitude regions, confidence is lower. IceBoost v2.0 demonstrates strong generalization at ice sheet margins. On the Geikie Plateau, East Greenland, we find nearly twice as much ice compared to BedMachine v3, highlighting the method's potential to refine the bed topography in parts of the ice sheets. The quality of the modeled ice thickness depends on the accuracy of the training data, the digital elevation model, ice velocity fields, and glacier geometries, including nunataks. We present the released dataset of ice thickness and associated uncertainty for all glaciers within the Randolph Glacier Inventory version 6 and 7, totaling half a million maps. This may be useful for modeling glacier dynamics, future evolution and sea-level rise, informing the design of glaciological surveys, field campaigns, as well as guiding policies on freshwater management.