Find the one's digit of the cube of the following number;

$53$

Observe the pattern;

$$\begin{gathered} 1^3=1=1 \\ {2}^3=8=3+5 \\ {3}^3=27=7+9+11 \\ {4}^3=64=13+15+17+19 \\ {5}^3=125=21+23+25+27+29 \end{gathered}$$

Express $6^3$ as the sum of odd numbers using above pattern.

Observe the pattern;

$$\begin{gathered} 1^3=1=1 \\ {2}^3=8=3+5 \\ {3}^3=27=7+9+11 \\ {4}^3=64=13+15+17+19 \\ {5}^3=125=21+23+25+27+29 \end{gathered}$$

Express $8^3$ as the sum of odd numbers using above pattern.

Observe the pattern;

$$\begin{gathered} 1^3=1=1 \\ {2}^3=8=3+5 \\ {3}^3=27=7+9+11 \\ {4}^3=64=13+15+17+19 \\ {5}^3=125=21+23+25+27+29 \end{gathered}$$

Express $7^3$ as the sum of odd numbers using above pattern.

Consider the following pattern. 

$2^3-1^3=1+2\times 1\times 3$

$3^3-2^3=1+3\times 2\times 3$

$4^3-3^3=1+4\times 3\times 3$

Using the above pattern, find the value of $7^3-6^3$.

Consider the following pattern. 

$2^3-1^3=1+2\times 1\times 3$

$3^3-2^3=1+3\times 2\times 3$

$4^3-3^3=1+4\times 3\times 3$

Using the above pattern, find the value of ${12}^3-{11}^3$.

Consider the following pattern. 

$2^3-1^3=1+2\times 1\times 3$

$3^3-2^3=1+3\times 2\times 3$

$4^3-3^3=1+4\times 3\times 3$

Using the above pattern, find the value of ${20}^3-{19}^3$.

Consider the following pattern. 

$2^3-1^3=1+2\times 1\times 3$

$3^3-2^3=1+3\times 2\times 3$

$4^3-3^3=1+4\times 3\times 3$

Using the above pattern, find the value of ${51}^3-{50}^3$.