Say True or False. Justify them.

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 :

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

Find the sum of the following series :

$51+52+53+\dots +92$

Find the sum of the following series :

$1+4+9+16+\dots +225$

Find the sum of the following series :

$6^2+7^2+8^2+\dots +{21}^2$

Find the sum of the following series :

${10}^3+{11}^3+{12}^3+\dots +{20}^3$

Find the sum of the following series :

$1+3+5+\dots +71$