This paper contributes to cubic aggregation operator and applications in decision-making problem. In this paper, we use Dombi operational laws and Heronian mean operators, to develop a new concept of cubic fuzzy Heronian mean Dombi aggregation operators, i.e., cubic fuzzy Heronian mean Dombi aggregation (CFHMDA), cubic fuzzy weighted Heronian mean Dombi aggregation (CFWHMDA), cubic fuzzy geometric Heronian mean Dombi aggregation (CFGHMDA), and cubic fuzzy weighted geometric Heronian mean Dombi aggregation (CFWGHMDA) operators. The proposed operators are not deal single aspect, but also deal with the relation between multi-aspects making them more effectively solving decision-making (MADM) problems. We proposed a new algorithm to solve a multi-attribute decision-making problem based on the developed operators. Finally, we solved a MADM problems with the cubic fuzzy Heronian mean Dombi aggregation operators.