Final answer:
The blue-colored grape cluster berry round cells observed in a Gram staining reaction indicate that the cells are Gram-positive, and the likely bacterium is Staphylococcus aureus.
Step-by-step explanation:
When a smear from a patient with abscesses and boils is subjected to Gram staining and the result is blue-colored grape cluster berry round cells, the outcome of the Gram staining reaction is that the cells are Gram-positive. The grape-like clusters of spherical cells, which turn purple after being stained with crystal violet and not decolorized even after the addition of the decolorizing agent, strong signal the presence of a Gram-positive bacterium. A likely bacterium with this description is Staphylococcus aureus, known for causing skin infections such as abscesses and boils, and presenting a grape-like cluster arrangement under the microscope. The purple coloration is due to the thick peptidoglycan layer in Gram-positive bacteria which retains the crystal violet dye after the Gram staining process.