Ice as a typical phase change material has the advantages of low cost, high latent heat and environmental friendliness, and the ice melting process under natural convective conditions is a fundamental study that has received wide attention. For the cubic ice cubes having different air contents, their melting characteristics becomes more complicated. The melting model of cubic ice under natural convection conditions was developed, which can accurately predict the time of the entire melting process. To validate the accuracy of the model, a series of melting experiments on cubic ice cubes are conducted and analyzed, with mass and air contents varied from 20 g to 50 g, and from 0 to 3.9 %, with a model error of less than ±20 %. Based on the maximum melt rate and the change in shape to a pyramid of cubic ice, the melting process can be divided into the initial melting, frustum-shaped, and pyramid-shaped stages. Varying the air content of the ice regulated the total melting time and the time proportion of the initial melting stage and the frustum-shaped stage of the ice. The proportion of time in the pyramid-shaped stage decreased from 64.3 % to 51.5 % for bubble ice with an air content of 3.9 % compared to clear ice. The proportion of time in the pyramid-shaped stage during the ice melting process is not significantly related to the air content and mass, and remains at approximately 27 %. Results of this study are meaningful for regulating the melting process and optimizing phase change energy storage technologies.