Here's what I had to do in order to install the xmlrpc extension on php 8 (from sury repos) on Ubuntu 16, as there is no package available via pecl or apt:
# build
git clone https://git.php.net/repository/pecl/networking/xmlrpc.git
export CPPFLAGS=-I/usr/include/libxml2/
cd xmlrpc && phpize && ./configure --with-expat && make && make install
# enable - this varies depending on your configuration; apache/nginx/fpm will also need to be restarted
echo "extension=xmlrpc.so" > /etc/php/8.0/mods-available/xmlrpc.ini
ln -s /etc/php/8.0/mods-available/xmlrpc.ini /etc/php/8.0/cli/conf.d/20-xmlrpc.ini
ln -s /etc/php/8.0/mods-available/xmlrpc.ini /etc/php/8.0/fpm/conf.d/20-xmlrpc.ini