Students' experience in using formulas for volumes is often limited to substituting numbers into given formulas. An activity presented in this article may help students make connections between the formulas for volumes of prisms and volumes of pyramids. In addition, some interesting facts from number theory arise, demonstrating strong connections between different areas of mathematics. A set of identical cubical building blocks, preferably in two colors, will be needed to complete the constructions described. It is important to note that while these activities are designed to discuss the ideas of volume of prisms and volumes of pyramids, some interesting facts from number theory may be emphasized for deeper analysis, and well-developed algebraic skills are crucial for successful generalization of the numerical examples considered. As a result, these investigations may emphasize for students some strong connections between different branches of mathematics, and promote their view of the subject as the harmonious structure of interrelated ideas. (Contains 6 figures.)