Do you really mean oven or is it in fact a Cooker (double oven & electric hob)? The calculation you have done is called applying Diversity - it assumes you are unlikely to use all the hob rings together for any length of time and thus the total current load can be lower than it otherwise might appear to be (it's 10 Amps plus 30% of the remainder). The fact you are quoting the 15kW figure suggests it is a cooker and not just a built-in double oven - I would be surprised if just a double oven got anywhere near 15kW. You cannot apply Diversity to an oven, you must use the actual quoted load.
In this case your basic maths do add up, but whether a 6mm cable is sufficient depends on other factors such as length of cable run, installation method, any bunching or insulation etc. not just the load applied. A sparks will know the correct de-rating factors to apply to the load calculation, might I respectfully suggest you ask the advice of one.
If it truly is a 15kW load then I'd be putting in a 10mm cable regardless, the socket can add another 3kW of load to the cable.
Is it a fuse or a circuit breaker that protects it? Many older fuse boxes only allow for a maximum of a 30A fuse and even then it can only go in the first position, right next to the main switch. If it's a circuit breaker then you can get 40A versions but you MUST ensure the cable can support the increased load or you cause a fire.