Some More Interesting Patterns

Using the given pattern, find the missing numbers.
$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+\mathrm{}{\_\_}_{}^2={21}^2$
$5^2+\mathrm{}{\_\_}_{}^2+{30}^2={31}^2$
$6^2+7^2+{\_\_}_{}^2={\_\_}_{}^2$

Observe the following pattern and supply the missing number.
                                            ${11}^2=121$
                                         ${101}^2=10201$
                                    ${10101}^2=102030201$
                                ${1010101}^2=.\dots \dots .......$
                               $...........{\dots }^2=10203040504030201$

Observe the following pattern and find the missing digits.
                 ${11}^2=121$
             ${101}^2=10201$
          ${1001}^2=1002001$
     ${100001}^2=1........2.........1$
${10000001}^2=\dots \dots \dots ........$