The positive integers which are multiple of 8 are:

8,16,24,................up to 15 terms

It forms an arithmetic series. 

Now

first term a = 8

common difference d = 8

number of terms n = 15

Now sum of first 15 terms of AP = (n/2) *{2a + (n-1)*d}

                                               = (15/2)*{2*8 + (15-1)*8}

                                               = (15/2)*(16 + 14*8)

                                               = (15/2)*(16 + 112)

                                               = (15*128)/2

                                               = 15*64                   (when 64 and 2 is divided by 2)

                                               = 960

So sum of first 15 terms which are multiple of 8 = 960