A great number of researchers, such as Marsh, Posner, Ross, Young, Wragg, Pinar, Moore, etc. explored the key concepts of curriculum: definitions and characteristics, planning and development, management, teaching perspectives, etc. Their works are of great value not only for those who are taking leading roles in policy making and implementation of the twenty first century curriculum in schools. Schools themselves should reflect on if the curriculum for their pupils changes the educational process corresponding to the crucial challenges of the knowledge society. Should community interest groups, parents, teachers and pupils take part in designing curriculum? What can have the power from the very early years at school to make the teaching/learning processes more fruitful and resulting in achieving competences which should make background for more successful life in the uncertain world of the future? Can the cubic curriculum help to do it? What opportunities and insufficiencies can cubic curriculum empower in primary schools? The paper presents curriculum not only as the program or teaching contents but as different pedagogical and organizational activities in and beyond primary school constructed according to the peculiar cubic curriculum model as well. Potentialities and inadequacies of planning and developing cubic curriculum in primary schools are disclosed. Presentation of the model of systematic spiral planning and development of cubic curriculum at primary school level makes the novelty of the paper.The paper consists of four parts. The first part conveys the overview of definitions of curriculum met in the works of the curriculum scientists and professionals. It substantiates the contemporary viewpoint why in the twenty first century the curriculum term is still tending to change. The paper analyses possible alternatives of its interpretation: the educational program with goals, contents, forms and methods of realization; an individual educational program; actions performed by the school community members. The second part presents the unique viewpoint of professor in Education E.C.Wragg at Exeter University who sees the curriculum as a cube having three principal dimensions of subject matter, cross-curricular themes and issues that influence children's general development and different methods of teaching and learning which can be employed. Curriculum in schools can be planned and developed according to the model of cubic curriculum. This viewpoint of cubic curriculum makes the methodological foundation of the paper. The third part analyses challenging aspects of implementation of cubic curriculum, peculiarities of planning and development it in primary schools. The paper substantiates that cubic curriculum proposes larger possibilities for incorporation of teaching for the future into the school curriculum. It displays the facts that school community influencing curriculum changes can transform and develop school into learning organization, develop pedagogical, methodological and didactic components of a school, raise the cumulative ICT competence of the school community, and enrich culture of the institution. The fourth part discloses the potentialities and inadequacies of planning and development of cubic curriculum in primary schools where every year content and different pedagogical and organizational activities in and beyond primary school are constructed in spiral method with the growing scope and parameters of the cubic curriculum area. The research results showing the role of the community interest groups, parents, teachers and pupils taking part in designing cubic curriculum are presented as well.