MySQL base64 custom implementation (as of version 5.6+ there are native ones: https://dev.mysql.com/doc/refman/5.6/en/string-functions.html#function_from-base64)

mysql-base64.sql

-- drop function if exists base64_encode;
create function base64_encode(_data blob)
returns text
begin
    declare _alphabet char(64) default 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/';
    declare _lim int unsigned default length(_data);
    declare _i int unsigned default 0;
    declare _chk3 char(6) default '';
    declare _chk3int int default 0;
    declare _enc text default '';
    
    while _i < _lim do
        set _chk3 = rpad(hex(binary substr(_data, _i + 1, 3)), 6, '0');
        set _chk3int = conv(_chk3, 16, 10);
        set _enc = concat(
            _enc
            ,                  substr(_alphabet, ((_chk3int >> 18) & 63) + 1, 1)
            , if (_lim-_i > 0, substr(_alphabet, ((_chk3int >> 12) & 63) + 1, 1), '=')
            , if (_lim-_i > 1, substr(_alphabet, ((_chk3int >>  6) & 63) + 1, 1), '=')
            , if (_lim-_i > 2, substr(_alphabet, ((_chk3int >>  0) & 63) + 1, 1), '=')
        );
        set _i = _i + 3;
    end while;
    
    return _enc;
end;

-- drop function if exists base64_decode;
create function base64_decode(_enc text)
returns blob
begin
    declare _alphabet char(64) default 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/';
    declare _lim int unsigned default 0;
    declare _i int unsigned default 0;
    declare _chr1byte tinyint default 0;
    declare _chk4int int default 0;
    declare _chk4int_bits tinyint default 0;
    declare _dec blob default '';
    declare _rem tinyint default 0;
    set _enc = trim(_enc);
    set _rem = if(right(_enc, 3) = '===', 3, if(right(_enc, 2) = '==', 2, if(right(_enc, 1) = '=', 1, 0)));
    set _lim = length(_enc) - _rem;
    
    while _i < _lim
    do
        set _chr1byte = locate(substr(_enc, _i + 1, 1), binary _alphabet) - 1;
        if (_chr1byte > -1)
        then
            set _chk4int = (_chk4int << 6) | _chr1byte;
            set _chk4int_bits = _chk4int_bits + 6;
            
            if (_chk4int_bits = 24 or _i = _lim-1)
            then
                if (_i = _lim-1 and _chk4int_bits != 24)
                then
                    set _chk4int = _chk4int << 0;
                end if;
                
                set _dec = concat(
                    _dec
                    ,                        char((_chk4int >> (_chk4int_bits -  8)) & 0xff)
                    , if(_chk4int_bits >  8, char((_chk4int >> (_chk4int_bits - 16)) & 0xff), '\0')
                    , if(_chk4int_bits > 16, char((_chk4int >> (_chk4int_bits - 24)) & 0xff), '\0')
                );
                set _chk4int = 0;
                set _chk4int_bits = 0;
            end if;
        end if;
        set _i = _i + 1;
    end while;
    
    return substr(_dec, 1, length(_dec) - _rem);
end;

-- example:

select  base64_encode('123') as `123`,
        base64_encode('1231') as `1231`,
        base64_encode('12312') as `12312`,
        base64_encode('123123') as `123123`,
        base64_encode('0123456789') as `0123456789`,
        base64_encode('ололо') as `ололо`,
        base64_encode('ёлка') as `ёлка`
union all
select  base64_decode(base64_encode('123')) as `123`,
        base64_decode(base64_encode('1231')) as `1231`,
        base64_decode(base64_encode('12312')) as `12312`,
        base64_decode(base64_encode('123123')) as `123123`,
        base64_decode(base64_encode('0123456789')) as `0123456789`,
        base64_decode(base64_encode('ололо')) as `ололо`,
        convert(base64_decode(base64_encode('ёлка')) using utf8) as `ёлка`;

I got a syntax error on line 5 trying on MySQL 5.5.59