How to add a number (ie. 8) to a date to output a date +8 days from starting date?

Numbers stores dates as date-time values rather than as serial numbers the way Excel does. To make working with dates easy, Numbers has a 'Duration' data format and related functions DURATION, DUR2DAYS, etc. that Excel doesn't have. When you have a valid date-time in a cell (right-aligned by default) you can simply "add" a simple integer to that and Numbers will assume that you mean days. You can use the DURATION() and Date and Time functions when you are adding something other than days. Explanations at Help > Formulas and Functions Help in your menu.

SG

Adding the other option SGII highlighted:

enter the date in a cell (let's say cell A1), then in another cell enter the formula

=A1+"8d"

or

= A1 + 8

or

=A1 +DURATION(0,8)

note... the Duration() function takes many arguments.

DURATION(weeks,days,hours,minutes,seconds,milliseconds)

since I really only wanted to provide days, I must include "weeks" which proceeds the argument "days". All the arguments after day, however, are not necessary, so I left them off and they default to the value zero. The equivalent would be:

DURATION(0,8,0,0,0,0)

enter the date in a cell (let's say cell A1), then in another cell enter the formula

=A1+"8d"

or

= A1 + 8