Question

Write the cubes of all natural numbers between 1 and 10 and verify the following statements:
(i) Cubes of all odd natural numbers are odd
(ii) Cubes of all even natual numbers are even.

Answer 1

Cubes of first 10 natural numbers:
$(1{)}^3=1\times 1\times 1=1(2{)}^3=2\times 2\times 2=8(3{)}^3=3\times 3\times 3=27(4{)}^3=4\times 4\times 4=64(5{)}^3=5\times 5\times 5=125(6{)}^3=6\times 6\times 6=216(7{)}^3=7\times 7\times 7=343(8{)}^3=8\times 8\times 8=512(9{)}^3=9\times 9\times 9=729(10{)}^3=10\times 10\times 10=1000$
We see that the cubes of odd numbers is also odd and cubes of even numbers is also even