Question : When $a=61, b=63$ and $c=65$, then what is the value of $a^3+b^3+c^3-3abc$?

Option 1: 1456

Option 2: 2268

Option 3: 4536

Option 4: 5460

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

Option 1: $a^2+b^2+c^2-3abc$

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

Question : If $a+b+c=7$ and $a^3+b^3+c^3-3abc=175$, then what is the value of $(a b+b c+c a)$?

Option 1: 8

Option 2: 9

Option 3: 7

Option 4: 6

Question : If $(a + b + c) = 13$ and $(ab + bc + ca) = 54$, find the value of $\left(a^2+b^2+c^2\right)$.

Option 1: 63

Option 2: 65

Option 3: 61

Option 4: 59

Question : If $a+b+c=15$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{71}{abc}$, then the value of $a^{3}+b^{3}+c^{3}-3abc$ is:

Option 1: 160

Option 2: 180

Option 3: 200

Option 4: 220

Question : If $a+b-c=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3-c^3+3abc$.

Option 1: 480

Option 2: 720

Option 3: 640

Option 4: 560