Formula use: \left(a+b\right)^3=a^3+3.a^2.b+3.a.b^2+b^3
Formula use: \left(a+b\right)^2=a^2+2.a.b+b^2

Explanation

Here, given expression is : a+b+2c
Now, we find the cubes with the help of formula :
\{\left(a\right)+\left(b+2c\right)\}^3
\rightarrow\left(a\right)^3+3.\left(a\right)^2.\left(b+2c\right)+3.a.\left(b+2c\right)^2+\left(b+2c\right)^3 _{[use formula]}
\rightarrow a^3+3a^2.\left(b+2c\right)+3a.\{\left(b\right)^2+2.b.2c+\left(2c\right)^2\}+\{\left(b\right)^3+3.\left(b\right)^2.2c+3.b.\left(2c\right)^2+\left(2c\right)^3\}
\rightarrow a^3+3a^2b+6a^2c+3a.\left(b^2+4bc+{4c}^2\right)+\left(b^3+6b^2c+12bc^2+{8c}^3\right)
\rightarrow a^3+3a^2b+6a^2c+3ab^2+12abc+12ac^2+b^3+6b^2c+12bc^2+{8c}^3
Ans: a^3+3a^2b+6a^2c+3ab^2+12abc+12ac^2+b^3+6b^2c+12bc^2+{8c}^3\ .