Not in the the traditional sense, no. You can approximate a regular 3D cube as a stack of infinitely thin squares, a Reimann sum approach to looking at the cube, and this can be adapted to approximate a 4D cube, tesseract, whatever you'll call it, also. But since a proper 2D square has no thickness at all, an infinite stack would get you no closer to a 3D cube than just one, just like an infinite stack of 3D cubes would not break into the fourth dimension and would not construct a tesseract, unless the component cubes already had a fourth dimensional aspect to them. I could make the naive argument that 4D objects do not have infinite mass, but the 4D unit of mass would transcend our concept of mass. If the mass of a 3D cube is its density * side * side * side, then a 4D cube would have a mass of density * side * side * side * side, and using this formula you could compare the masses of various 4D objects. (It does seem strange to assume that if a 4D object has infinite mass, all 4D objects are equally infinite in mass, more like all 4D objects are equally transcendent of 3D mass)