Volume of rectangular box

= \( \Large 10 \times 8 \times 6 = 480 cm^{2}\)

= \( \Large 6240 cm^{3} \)

= \( \Large \frac{Volume \ of \ cubes}{Volume \ of \ rectangular \ box} \)

= \( \Large \frac{6240}{480} = 13 \)

Hence, 13 boxes are needed.