Observation and analysis of cancer cell behaviour in 3D environment is essential for full understanding of the mechanisms of cancer cell invasion. However, label-free imaging of live cells in 3D conditions is optically more challenging than in 2D. Quantitative phase imaging provided by coherence controlled holographic microscopy produces images with enhanced information compared to ordinary light microscopy and, due to inherent coherence gate effect, enables observation of live cancer cells' activity even in scattering milieu such as the 3D collagen matrix. Exploiting the dynamic phase differences method, we for the first time describe dynamics of differences in cell mass distribution in 3D migrating mesenchymal and amoeboid cancer cells, and also demonstrate that certain features are shared by both invasion modes. We found that amoeboid fibrosarcoma cells' membrane blebbing is enhanced upon constriction and is also occasionally present in mesenchymally invading cells around constricted nuclei. Further, we demonstrate that both leading protrusions and leading pseudopods of invading fibrosarcoma cells are defined by higher cell mass density. In addition, we directly document bundling of collagen fibres by protrusions of mesenchymal fibrosarcoma cells. Thus, such a non-invasive microscopy offers a novel insight into cellular events during 3D invasion.