The three-way ANOVA is used to determine if there is an interaction effect (independent variables interact if the effect of one of the variables differs depending on the level of the other variable) between three independent variables on a continuous dependent variable.
Therefore you would only be interested in the significance value of ABC. If it is significant, you would report that there is a 3-way interaction which means that at least one of the 2-way interactions changes across the third independent variable. If ABC is not significant, it would be better to apply 2-way ANOVA.
Because when interaction effects are present, it means that interpretation of the main effects or underlying lower level interactions is incomplete or misleading. Hence the significances of A, B, C, AB, BC, A*C are not important.