The binary number \(101_{two}\) is equivalent to the decimal number 5. Therefore, \((101_{two})^3\) is equivalent to \(5^3\), which is 125 in decimal.

Now, let's convert 125 to binary:

125 / 2 = 62 remainder 1 (least significant bit)
62 / 2 = 31 remainder 0
31 / 2 = 15 remainder 1
15 / 2 = 7 remainder 1
7 / 2 = 3 remainder 1
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1 (most significant bit)

So, 125 in decimal is \(1111101_{two}\) in binary. Therefore, \((101_{two})^3\) is \(1111101_{two}\).