Using translation concepts, the equation will be given by:
[tex]g(x) = (x + 8)^3 + 3[/tex]
The parent function is:
[tex]f(x) = x^3[/tex]
Shifting a function left 8 units means that [tex]g(x) = f(x + 8)[/tex], hence:
[tex]g(x) = f(x + 8) = (x + 8)^3[/tex]
Shifting a function up 3 units means that 3 is added to the function, that is, [tex]g(x) = f(x + 8) + 3[/tex], hence:
[tex]g(x) = f(x + 8) + 3 = (x + 8)^3 + 3[/tex]
Which is the desired equation.
You can learn more about translation concepts at https://brainly.com/question/4521517