First we need to write the balanced chemical equation:

  2H\(_2\) +  O\(_2\) →  2H\(_2\)O

Reacting moles:  2 moles :  1 moles  2 moles

Expected reacting Volume: 8 cm\(^3\):  20 cm\(^3\)

Actual reacted Volume: 8 cm\(^3\): 4cm\(^3\)  (Based on the balanced equation)

Residual Volume(Expected - Actual):  0cm\(^3\) :  16cm\(^3\)

Therefore, 16cm\(^3\) of Oxygen will remain after reacting 8cm\(^3\) of hydrogen gas with 20cm\(^3\) of oxygen gas.