How many squares are there in a standard chess board?

Say True or False. Justify them.

The sum of first $n$ odd natural numbers is always an odd number.

Say True or False. Justify them.

The sum of consecutive even numbers is always an even number.

The difference between the sum of squares of first $n$ natural numbers and the sum of first $n$ natural numbers is always divisible by $2$.

The sum of cubes of the first $n$ natural numbers is always a square number.

Find the sum of the following series :

$1+2+3+\dots +60$

Find the sum of the following series :

$3+6+9+\dots +96$