In this paper, firstly, novel approaches of score function and accuracy function are introduced to achieve more practical and convincing comparison results of two neutrosophic cubic values. Furthermore, the neutrosophic cubic Hamacher weighted averaging operator and the neutrosophic cubic Hamacher weighted geometric operator are developed to aggregate neutrosophic cubic values. Some desirable properties of these operators such as idempotency, monotonicity and boundedness are discussed. To deal with the multi-criteria decision making problems in which attribute values take the form of the neutrosophic cubic elements, the decision making algorithms based on some Hamacher aggregation operators, which are extensions of the algebraic aggregation operators and Einstein aggregation operators, are constructed. Finally, the illustrative examples and comparisons are given to verify the proposed algorithms and to demonstrate their practicality and effectiveness.