Solution

(i) Cube of any odd number is even.
FALSE: Odd multiplied by odd is always odd

(ii) A perfect cube does not end with two zeros.

TRUE: A perfect cube will end with odd number of zeroes

(iii) If square of a number ends with $$5$$, then its cube ends with $$25$$.

TRUE: $$5$$ multiplied by $$5$$ any number of times always gives $$5$$ at units place

(iv) There is no perfect cube which ends with $$8$$.

False: $$ 2^{3} =8 $$

(v) The cube of a two digit number may be a three digit number.

FALSE: The smallest two digit number is $$10$$ and $$10^{3} $$ $$=1000$$ is a three digit number

(vi) The cube of a two digit number may have seven or more digits.

FALSE: $$99$$ is the largest $$2$$ digit number; $$ 99^{3} $$ $$=989901$$ is a $$6$$ digit number

(vii) The cube of a single digit number may be a single digit number.

TRUE: $$ 2^{3} = 8 $$ is a single digit number.