High Order Buttersworth Filter
The impulse response of two filters in series is the convolution of each filters impulse response. You can multiply two polynomials by convolving their coefficients. Likewise you can factor or combine filters by factoring or multiplying their transfer functions described as polynomials.  For example, a fourth order filter can be factored into two 2nd order filters in series, or two 2nd order filters can be combined into one fourth order filter- it’s simply polynomial multiplication or factoring.

So in your case since you already factored the Butterworth filter into individual filters that you know how to implement, you would then simply cascade those filters.

As @MattL points out in the comments, you must pay careful attention to impedances when cascading analog filter sections. In the analog such structures are quite common with active filter design where it is quite simple to isolate the sections with appropriate design techniques, but not so common with filters constructed with passive components.